diff --git a/Lib/test/string_tests.py b/Lib/test/string_tests.py
index 8d210b198d248d..5c859400ed943b 100644
--- a/Lib/test/string_tests.py
+++ b/Lib/test/string_tests.py
@@ -323,12 +323,14 @@ def test_rindex(self):
 
     def test_find_periodic_pattern(self):
         """Cover the special path for periodic patterns."""
-        def reference_find(p, s):
-            for i in range(len(s)):
-                if s.startswith(p, i):
+        def reference_find(text, p):
+            for i in range(len(text) - len(p) + 1):
+                if text.startswith(p, i):
                     return i
             return -1
 
+        short = ['', 'a', 'b', 'ab', 'ba', 'aab', 'aba', 'baa']
+        pairs = [(text, p) for text in short for p in short]
         rr = random.randrange
         choices = random.choices
         for _ in range(1000):
@@ -337,8 +339,10 @@ def reference_find(p, s):
             left = ''.join(choices('abcdef', k=rr(2000)))
             right = ''.join(choices('abcdef', k=rr(2000)))
             text = left + p + right
+            pairs.append((text, p))
+        for text, p in pairs:
             with self.subTest(p=p, text=text):
-                self.checkequal(reference_find(p, text),
+                self.checkequal(reference_find(text, p),
                                 text, 'find', p)
 
     def test_find_many_lengths(self):
diff --git a/Misc/NEWS.d/next/Tests/2023-06-10-22-24-34.gh-issue-105639.Zg6a5c.rst b/Misc/NEWS.d/next/Tests/2023-06-10-22-24-34.gh-issue-105639.Zg6a5c.rst
new file mode 100644
index 00000000000000..a5419019d6d84d
--- /dev/null
+++ b/Misc/NEWS.d/next/Tests/2023-06-10-22-24-34.gh-issue-105639.Zg6a5c.rst
@@ -0,0 +1 @@
+Fixed an intermittent test failure in ``test_find_periodic_pattern`` from the ``string_tests`` module.