diff --git a/CHANGELOG.md b/CHANGELOG.md
index bca8b63b..4416e5fe 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -17,6 +17,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 ### Changed
 
 - CI: enable setting python version for package build ([#244](https://github.com/Lightning-AI/utilities/pull/244))
+- docs: fix/use PyPI versions for pinning links ([#243](https://github.com/Lightning-AI/utilities/pull/243))
 
 
 ### Deprecated
@@ -26,7 +27,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 
 ### Fixed
 
-- docs: fix/use PyPI versions for pinning links ([#243](https://github.com/Lightning-AI/utilities/pull/243))
+- docs: do not replace external link for self ([#245](https://github.com/Lightning-AI/utilities/pull/245))
 
 
 ## [0.11.0] - 2024-03-18
diff --git a/docs/source/conf.py b/docs/source/conf.py
index a3007a04..1e64f57f 100644
--- a/docs/source/conf.py
+++ b/docs/source/conf.py
@@ -46,10 +46,10 @@
 # -- Project documents -------------------------------------------------------
 
 fetch_external_assets(docs_folder=_PATH_HERE)
+
+adjust_linked_external_docs("https://numpy.org/doc/stable/", "https://numpy.org/doc/{numpy.__version__}/", _PATH_HERE)
 adjust_linked_external_docs(
-    source_link="https://numpy.org/doc/stable/",
-    target_link="https://numpy.org/doc/{numpy.__version__}/",
-    browse_folder=_PATH_HERE,
+    "https://pytorch.org/docs/stable/", "https://pytorch.org/docs/{torch.__version__}/", _PATH_HERE
 )
 
 
diff --git a/src/lightning_utilities/docs/formatting.py b/src/lightning_utilities/docs/formatting.py
index 32f616ac..881339b6 100644
--- a/src/lightning_utilities/docs/formatting.py
+++ b/src/lightning_utilities/docs/formatting.py
@@ -157,10 +157,21 @@ def adjust_linked_external_docs(
     # replace the source link with target link
     for fpath in set(list_files):
         with open(fpath, encoding="UTF-8") as fopen:
-            body = fopen.read()
-        body_ = body.replace(source_link, target_link)
-        if body == body_:
+            lines = fopen.readlines()
+        found, skip = False, False
+        for i, ln in enumerate(lines):
+            # prevent the replacement its own function calls
+            if f"{adjust_linked_external_docs.__name__}(" in ln:
+                skip = True
+            if not skip and source_link in ln:
+                # replace the link if any found
+                lines[i] = ln.replace(source_link, target_link)
+                # record the found link for later write file
+                found = True
+            if skip and ")" in ln:
+                skip = False
+        if not found:
             continue
         logging.debug(f'links adjusting in {fpath}: "{source_link}" -> "{target_link}"')
         with open(fpath, "w", encoding="UTF-8") as fw:
-            fw.write(body_)
+            fw.writelines(lines)