diff --git a/nltk/metrics/distance.py b/nltk/metrics/distance.py
index 1f3211bd03..c5af07cb38 100644
--- a/nltk/metrics/distance.py
+++ b/nltk/metrics/distance.py
@@ -99,14 +99,19 @@ def edit_distance(s1, s2, substitution_cost=1, transpositions=False):
     last_left_t = _last_left_t_init(sigma)
 
     # iterate over the array
-    for i in range(len1):
-        last_right = 0
-        for j in range(len2):
-            last_left = last_left_t[s2[j]]
+    # i and j start from 1 and not 0 to stay close to the wikipedia pseudo-code
+    # see https://en.wikipedia.org/wiki/Damerau%E2%80%93Levenshtein_distance
+    for i in range(1, len1 + 1):
+        last_right_buf = 0
+        for j in range(1, len2 + 1):
+            last_left = last_left_t[s2[j - 1]]
+            last_right = last_right_buf
+            if s1[i - 1] == s2[j - 1]:
+                last_right_buf = j
             _edit_dist_step(
                 lev,
-                i + 1,
-                j + 1,
+                i,
+                j,
                 s1,
                 s2,
                 last_left,
@@ -114,9 +119,7 @@ def edit_distance(s1, s2, substitution_cost=1, transpositions=False):
                 substitution_cost=substitution_cost,
                 transpositions=transpositions,
             )
-            if s1[i] == s2[j]:
-                last_right = j + 1
-            last_left_t[s1[i]] = i + 1
+        last_left_t[s1[i - 1]] = i
     return lev[len1][len2]
 
 
diff --git a/nltk/test/unit/test_distance.py b/nltk/test/unit/test_distance.py
index 23a5b9c4fc..96d814d0b8 100644
--- a/nltk/test/unit/test_distance.py
+++ b/nltk/test/unit/test_distance.py
@@ -94,6 +94,12 @@ class TestEditDistance:
             # (but cost 5 if substitution_cost=2)
             ("kitten", "sitting", 1, (3, 3)),
             ("kitten", "sitting", 2, (5, 5)),
+            #
+            # duplicated letter
+            # e.g. "duplicated" -D-> "duplicated"
+            ("duplicated", "duuplicated", 1, (1, 1)),
+            ("duplicated", "duuplicated", 2, (1, 1)),
+            ("very duplicated", "very duuplicateed", 2, (2, 2)),
         ],
     )
     def test_with_transpositions(