diff --git a/h2/src/docsrc/html/changelog.html b/h2/src/docsrc/html/changelog.html
index c4b9881605..618e13df7b 100644
--- a/h2/src/docsrc/html/changelog.html
+++ b/h2/src/docsrc/html/changelog.html
@@ -21,6 +21,8 @@ <h1>Change Log</h1>
 
 <h2>Next Version (unreleased)</h2>
 <ul>
+<li>Issue #4036: NULLS NOT DISTINCT constraint changed after column dropped
+</li>
 <li>Issue #4033: Wrong array produced when using ARRAY_AGG() on UNNEST(ARRAY[CAST(? AS INT)]) expression
 in a PreparedStatement
 </li>
diff --git a/h2/src/main/org/h2/constraint/ConstraintUnique.java b/h2/src/main/org/h2/constraint/ConstraintUnique.java
index 7ec2ea2ffe..0fa08660cb 100644
--- a/h2/src/main/org/h2/constraint/ConstraintUnique.java
+++ b/h2/src/main/org/h2/constraint/ConstraintUnique.java
@@ -53,8 +53,11 @@ private String getCreateSQLForCopy(Table forTable, String quotedName, boolean in
             builder.append(" COMMENT ");
             StringUtils.quoteStringSQL(builder, comment);
         }
-        builder.append(' ').append(getConstraintType().getSqlName()).append('(');
-        IndexColumn.writeColumns(builder, columns, DEFAULT_SQL_FLAGS).append(')');
+        builder.append(' ').append(getConstraintType().getSqlName());
+        if (!primaryKey) {
+            nullsDistinct.getSQL(builder.append(' '), DEFAULT_SQL_FLAGS).append(' ');
+        }
+        IndexColumn.writeColumns(builder.append('('), columns, DEFAULT_SQL_FLAGS).append(')');
         if (internalIndex && indexOwner && forTable == this.table) {
             builder.append(" INDEX ");
             index.getSQL(builder, DEFAULT_SQL_FLAGS);
diff --git a/h2/src/test/org/h2/test/scripts/ddl/createTable.sql b/h2/src/test/org/h2/test/scripts/ddl/createTable.sql
index 0e4db7d43e..93004fa045 100644
--- a/h2/src/test/org/h2/test/scripts/ddl/createTable.sql
+++ b/h2/src/test/org/h2/test/scripts/ddl/createTable.sql
@@ -267,5 +267,17 @@ SELECT CONSTRAINT_NAME, NULLS_DISTINCT, INDEX_NAME FROM INFORMATION_SCHEMA.TABLE
 > CONSTRAINT_273C NO             CONSTRAINT_INDEX_273C
 > rows: 4
 
+ALTER TABLE TEST ADD COLUMN E BIGINT;
+> ok
+
+SELECT CONSTRAINT_NAME, NULLS_DISTINCT, INDEX_NAME FROM INFORMATION_SCHEMA.TABLE_CONSTRAINTS WHERE TABLE_NAME = 'TEST';
+> CONSTRAINT_NAME NULLS_DISTINCT INDEX_NAME
+> --------------- -------------- -----------------------
+> CONSTRAINT_2    YES            CONSTRAINT_2_INDEX_D
+> CONSTRAINT_27   YES            CONSTRAINT_27_INDEX_D
+> CONSTRAINT_273  YES            CONSTRAINT_273_INDEX_D
+> CONSTRAINT_273C NO             CONSTRAINT_273C_INDEX_D
+> rows: 4
+
 DROP TABLE TEST;
 > ok
diff --git a/h2/src/test/org/h2/test/scripts/functions/system/db_object.sql b/h2/src/test/org/h2/test/scripts/functions/system/db_object.sql
index c9aefe2e22..fae11ec345 100644
--- a/h2/src/test/org/h2/test/scripts/functions/system/db_object.sql
+++ b/h2/src/test/org/h2/test/scripts/functions/system/db_object.sql
@@ -234,7 +234,7 @@ SELECT T, ID_A <> ID_B, SQL_A, SQL_B FROM (VALUES
 )) T(T, ID_A, ID_B, SQL_A, SQL_B);
 > T          ID_A <> ID_B SQL_A                                                                                                                           SQL_B
 > ---------- ------------ ------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------
-> CONSTRAINT TRUE         ALTER TABLE "PUBLIC"."T_A" ADD CONSTRAINT "PUBLIC"."C_A" UNIQUE("ID")                                                           ALTER TABLE "PUBLIC"."T_B" ADD CONSTRAINT "PUBLIC"."C_B" UNIQUE("ID")
+> CONSTRAINT TRUE         ALTER TABLE "PUBLIC"."T_A" ADD CONSTRAINT "PUBLIC"."C_A" UNIQUE NULLS DISTINCT ("ID")                                           ALTER TABLE "PUBLIC"."T_B" ADD CONSTRAINT "PUBLIC"."C_B" UNIQUE NULLS DISTINCT ("ID")
 > INDEX      TRUE         CREATE UNIQUE NULLS DISTINCT INDEX "PUBLIC"."I_A" ON "PUBLIC"."T_A"("ID" NULLS FIRST)                                           CREATE UNIQUE NULLS DISTINCT INDEX "PUBLIC"."I_B" ON "PUBLIC"."T_B"("ID" NULLS FIRST)
 > SYNONYM    TRUE         CREATE SYNONYM "PUBLIC"."S_A" FOR "PUBLIC"."T_A"                                                                                CREATE SYNONYM "PUBLIC"."S_B" FOR "PUBLIC"."T_B"
 > TABLE      TRUE         CREATE MEMORY TABLE "PUBLIC"."T_A"( "ID" INTEGER )                                                                              CREATE MEMORY TABLE "PUBLIC"."T_B"( "ID" INTEGER )
diff --git a/h2/src/test/org/h2/test/scripts/testScript.sql b/h2/src/test/org/h2/test/scripts/testScript.sql
index b860d3eaa1..208507f15d 100644
--- a/h2/src/test/org/h2/test/scripts/testScript.sql
+++ b/h2/src/test/org/h2/test/scripts/testScript.sql
@@ -6266,7 +6266,7 @@ SCRIPT NOPASSWORDS NOSETTINGS NOVERSION;
 > CREATE USER IF NOT EXISTS "SA" PASSWORD '' ADMIN;
 > CREATE MEMORY TABLE "PUBLIC"."TEST"( "A_INT" INTEGER NOT NULL, "B_INT" INTEGER NOT NULL );
 > -- 0 +/- SELECT COUNT(*) FROM PUBLIC.TEST;
-> ALTER TABLE "PUBLIC"."TEST" ADD CONSTRAINT "PUBLIC"."U_B" UNIQUE("B_INT");
+> ALTER TABLE "PUBLIC"."TEST" ADD CONSTRAINT "PUBLIC"."U_B" UNIQUE NULLS DISTINCT ("B_INT");
 > ALTER TABLE "PUBLIC"."TEST" ADD CONSTRAINT "PUBLIC"."C1" FOREIGN KEY("A_INT") REFERENCES "PUBLIC"."TEST"("B_INT") NOCHECK;
 > rows (ordered): 5
 
@@ -6418,9 +6418,9 @@ SCRIPT NOPASSWORDS NOSETTINGS NOVERSION;
 > INSERT INTO "PUBLIC"."B_TEST" VALUES (-1, 'XX');
 > ALTER TABLE "PUBLIC"."A_TEST" ADD CONSTRAINT "PUBLIC"."MIN_LENGTH" CHECK(CHAR_LENGTH("A_VARCHAR") > 1) NOCHECK;
 > ALTER TABLE "PUBLIC"."B_TEST" ADD CONSTRAINT "PUBLIC"."CONSTRAINT_76" CHECK(CHAR_LENGTH("B_VARCHAR") > 1) NOCHECK;
-> ALTER TABLE "PUBLIC"."A_TEST" ADD CONSTRAINT "PUBLIC"."DATE_UNIQUE" UNIQUE("A_DATE");
-> ALTER TABLE "PUBLIC"."A_TEST" ADD CONSTRAINT "PUBLIC"."DATE_UNIQUE_2" UNIQUE("A_DATE");
-> ALTER TABLE "PUBLIC"."B_TEST" ADD CONSTRAINT "PUBLIC"."B_UNIQUE" UNIQUE("B_INT");
+> ALTER TABLE "PUBLIC"."A_TEST" ADD CONSTRAINT "PUBLIC"."DATE_UNIQUE" UNIQUE NULLS DISTINCT ("A_DATE");
+> ALTER TABLE "PUBLIC"."A_TEST" ADD CONSTRAINT "PUBLIC"."DATE_UNIQUE_2" UNIQUE NULLS DISTINCT ("A_DATE");
+> ALTER TABLE "PUBLIC"."B_TEST" ADD CONSTRAINT "PUBLIC"."B_UNIQUE" UNIQUE NULLS DISTINCT ("B_INT");
 > ALTER TABLE "PUBLIC"."B_TEST" ADD CONSTRAINT "PUBLIC"."C3" FOREIGN KEY("B_INT") REFERENCES "PUBLIC"."A_TEST"("A_INT") ON DELETE SET DEFAULT ON UPDATE SET DEFAULT NOCHECK;
 > rows (ordered): 14
 
@@ -6521,8 +6521,8 @@ SCRIPT SIMPLE NOPASSWORDS NOSETTINGS NOVERSION;
 > INSERT INTO "PUBLIC"."CHILD" VALUES(101, 3, 1, 'Sabine');
 > INSERT INTO "PUBLIC"."CHILD" VALUES(200, NULL, NULL, 'Jim');
 > INSERT INTO "PUBLIC"."CHILD" VALUES(201, NULL, NULL, 'Johann');
-> ALTER TABLE "PUBLIC"."CHILD" ADD CONSTRAINT "PUBLIC"."CONSTRAINT_3" UNIQUE("ID", "PARENTID");
-> ALTER TABLE "PUBLIC"."PARENT" ADD CONSTRAINT "PUBLIC"."CONSTRAINT_8" UNIQUE("ID", "FAMILY_ID");
+> ALTER TABLE "PUBLIC"."CHILD" ADD CONSTRAINT "PUBLIC"."CONSTRAINT_3" UNIQUE NULLS DISTINCT ("ID", "PARENTID");
+> ALTER TABLE "PUBLIC"."PARENT" ADD CONSTRAINT "PUBLIC"."CONSTRAINT_8" UNIQUE NULLS DISTINCT ("ID", "FAMILY_ID");
 > ALTER TABLE "PUBLIC"."CHILD" ADD CONSTRAINT "PUBLIC"."PARENT_CHILD" FOREIGN KEY("PARENTID", "FAMILY_ID") REFERENCES "PUBLIC"."PARENT"("ID", "FAMILY_ID") ON DELETE SET NULL ON UPDATE CASCADE NOCHECK;
 > ALTER TABLE "PUBLIC"."PARENT" ADD CONSTRAINT "PUBLIC"."PARENT_FAMILY" FOREIGN KEY("FAMILY_ID") REFERENCES "PUBLIC"."FAMILY"("ID") NOCHECK;
 > rows (ordered): 19
@@ -6548,8 +6548,8 @@ SCRIPT SIMPLE NOPASSWORDS NOSETTINGS NOVERSION;
 > INSERT INTO "PUBLIC"."CHILD" VALUES(101, 3, 1, 'Sabine');
 > INSERT INTO "PUBLIC"."CHILD" VALUES(200, NULL, NULL, 'Jim');
 > INSERT INTO "PUBLIC"."CHILD" VALUES(201, NULL, NULL, 'Johann');
-> ALTER TABLE "PUBLIC"."CHILD" ADD CONSTRAINT "PUBLIC"."CONSTRAINT_3" UNIQUE("ID", "PARENTID");
-> ALTER TABLE "PUBLIC"."PARENT" ADD CONSTRAINT "PUBLIC"."CONSTRAINT_8" UNIQUE("ID", "FAMILY_ID");
+> ALTER TABLE "PUBLIC"."CHILD" ADD CONSTRAINT "PUBLIC"."CONSTRAINT_3" UNIQUE NULLS DISTINCT ("ID", "PARENTID");
+> ALTER TABLE "PUBLIC"."PARENT" ADD CONSTRAINT "PUBLIC"."CONSTRAINT_8" UNIQUE NULLS DISTINCT ("ID", "FAMILY_ID");
 > ALTER TABLE "PUBLIC"."PARENT" ADD CONSTRAINT "PUBLIC"."PARENT_FAMILY" FOREIGN KEY("FAMILY_ID") REFERENCES "PUBLIC"."FAMILY"("ID") NOCHECK;
 > rows (ordered): 18