diff --git a/packages/babel-helper-create-class-features-plugin/src/index.js b/packages/babel-helper-create-class-features-plugin/src/index.js
index d23c12cefdc1..e1d2222e8d24 100644
--- a/packages/babel-helper-create-class-features-plugin/src/index.js
+++ b/packages/babel-helper-create-class-features-plugin/src/index.js
@@ -120,6 +120,18 @@ export function createClassFeaturePlugin({
           }
 
           if (!isDecorated) isDecorated = hasOwnDecorators(path.node);
+
+          if (path.isStaticBlock()) {
+            throw path.buildCodeFrameError(`Incorrect plugin orders, \`@babel/plugin-proposal-class-static-block\` should be placed before class features plugins
+{
+  "plugins": [
+    "@babel/plugin-proposal-class-static-block",
+    "@babel/plugin-proposal-private-property-in-object",
+    "@babel/plugin-proposal-private-methods",
+    "@babel/plugin-proposal-class-properties",
+  ]
+}`);
+          }
         }
 
         if (!props.length && !isDecorated) return;
@@ -188,7 +200,12 @@ export function createClassFeaturePlugin({
       },
 
       PrivateName(path) {
-        if (this.file.get(versionKey) !== version) return;
+        if (
+          this.file.get(versionKey) !== version ||
+          path.parentPath.isPrivate({ key: path.node })
+        ) {
+          return;
+        }
 
         throw path.buildCodeFrameError(`Unknown PrivateName "${path}"`);
       },
diff --git a/packages/babel-plugin-proposal-class-static-block/test/plugin-ordering.test.js b/packages/babel-plugin-proposal-class-static-block/test/plugin-ordering.test.js
index 3839d8d72837..784428773d36 100644
--- a/packages/babel-plugin-proposal-class-static-block/test/plugin-ordering.test.js
+++ b/packages/babel-plugin-proposal-class-static-block/test/plugin-ordering.test.js
@@ -21,14 +21,14 @@ describe("plugin ordering", () => {
           proposalClassStaticBlock,
         ],
       });
-    }).toThrowErrorMatchingInlineSnapshot(`
-"/Users/jh/code/babel/example.js: Incorrect plugin orders, \`@babel/plugin-proposal-class-static-block\` should be placed before class features plugins
+    })
+      .toThrow(`Incorrect plugin orders, \`@babel/plugin-proposal-class-static-block\` should be placed before class features plugins
 {
-  \\"plugins\\": [
-    \\"@babel/plugin-proposal-class-static-block\\",
-    \\"@babel/plugin-proposal-private-property-in-object\\",
-    \\"@babel/plugin-proposal-private-methods\\",
-    \\"@babel/plugin-proposal-class-properties\\",
+  "plugins": [
+    "@babel/plugin-proposal-class-static-block",
+    "@babel/plugin-proposal-private-property-in-object",
+    "@babel/plugin-proposal-private-methods",
+    "@babel/plugin-proposal-class-properties",
   ]
 }
   1 | class Foo {
@@ -36,7 +36,6 @@ describe("plugin ordering", () => {
     |   ^
   3 |     this.foo = Foo.bar;
   4 |   }
-  5 |   static bar = 42;"
-`);
+  5 |   static bar = 42;`);
   });
 });