diff --git a/python/python-psi-impl/src/com/jetbrains/python/codeInsight/completion/PyParameterizedTypeInsertHandler.java b/python/python-psi-impl/src/com/jetbrains/python/codeInsight/completion/PyParameterizedTypeInsertHandler.java
index c060d44522d4..7dfca51696b1 100644
--- a/python/python-psi-impl/src/com/jetbrains/python/codeInsight/completion/PyParameterizedTypeInsertHandler.java
+++ b/python/python-psi-impl/src/com/jetbrains/python/codeInsight/completion/PyParameterizedTypeInsertHandler.java
@@ -19,7 +19,7 @@ public class PyParameterizedTypeInsertHandler extends ParenthesesInsertHandler<L
   public static boolean isCompletingParameterizedType(@NotNull PsiElement definition,
                                                       @NotNull PsiElement completionPosition,
                                                       @NotNull TypeEvalContext context) {
-    return PyTypingTypeProvider.isInsideTypeHint(completionPosition, context) && isParameterizedType(definition, context);
+    return PyTypingTypeProvider.isInsideTypeHint(completionPosition, context) && isParameterizableType(definition, context);
   }
 
   public static final PyParameterizedTypeInsertHandler INSTANCE = new PyParameterizedTypeInsertHandler();
@@ -33,8 +33,8 @@ public class PyParameterizedTypeInsertHandler extends ParenthesesInsertHandler<L
     return true;
   }
 
-  private static boolean isParameterizedType(@NotNull PsiElement element, @NotNull TypeEvalContext typeEvalContext) {
+  private static boolean isParameterizableType(@NotNull PsiElement element, @NotNull TypeEvalContext typeEvalContext) {
     return element instanceof PyQualifiedNameOwner qnOwner && PyTypingTypeProvider.GENERIC_CLASSES.contains(qnOwner.getQualifiedName()) ||
-           element instanceof PyClass pyClass && PyTypingTypeProvider.isGeneric(pyClass, typeEvalContext);
+           element instanceof PyClass pyClass && new PyTypingTypeProvider().getGenericType(pyClass, typeEvalContext) != null;
   }
 }
diff --git a/python/testData/completion/squareBracketsNotInsertedAfterAlreadyParameterizedGenericInsideTypeHints/a.after.py b/python/testData/completion/squareBracketsNotInsertedAfterAlreadyParameterizedGenericInsideTypeHints/a.after.py
new file mode 100644
index 000000000000..0fcf21de9e35
--- /dev/null
+++ b/python/testData/completion/squareBracketsNotInsertedAfterAlreadyParameterizedGenericInsideTypeHints/a.after.py
@@ -0,0 +1,8 @@
+from typing import Iterable
+
+
+class StrIterable(Iterable[str]):
+    pass
+
+
+x: StrIterable
\ No newline at end of file
diff --git a/python/testData/completion/squareBracketsNotInsertedAfterAlreadyParameterizedGenericInsideTypeHints/a.py b/python/testData/completion/squareBracketsNotInsertedAfterAlreadyParameterizedGenericInsideTypeHints/a.py
new file mode 100644
index 000000000000..c072759eebe3
--- /dev/null
+++ b/python/testData/completion/squareBracketsNotInsertedAfterAlreadyParameterizedGenericInsideTypeHints/a.py
@@ -0,0 +1,8 @@
+from typing import Iterable
+
+
+class StrIterable(Iterable[str]):
+    pass
+
+
+x: StrIter<caret>
\ No newline at end of file
diff --git a/python/testSrc/com/jetbrains/python/Py3CompletionTest.java b/python/testSrc/com/jetbrains/python/Py3CompletionTest.java
index c0483c0f4373..4e7c9cc1d4ec 100644
--- a/python/testSrc/com/jetbrains/python/Py3CompletionTest.java
+++ b/python/testSrc/com/jetbrains/python/Py3CompletionTest.java
@@ -743,6 +743,11 @@ public class Py3CompletionTest extends PyTestCase {
     doMultiFileTest();
   }
 
+  // PY-73246
+  public void testSquareBracketsNotInsertedAfterAlreadyParameterizedGenericInsideTypeHints() {
+    doMultiFileTest();
+  }
+
   private void doTestVariants(String @NotNull ... expected) {
     final String testName = getTestName(true);
     myFixture.configureByFile(testName + ".py");