diff --git a/doc/make.py b/doc/make.py
index 23b18d69acc04..878781c18a668 100755
--- a/doc/make.py
+++ b/doc/make.py
@@ -123,14 +123,14 @@ def _sphinx_build(self, kind: str):
 
         Parameters
         ----------
-        kind : {'html', 'latex', 'linkcheck'}
+        kind : {'html', 'latex'}
 
         Examples
         --------
         >>> DocBuilder(num_jobs=4)._sphinx_build('html')
         """
-        if kind not in ("html", "latex", "linkcheck"):
-            raise ValueError(f"kind must be html, latex or linkcheck, not {kind}")
+        if kind not in ("html", "latex"):
+            raise ValueError(f"kind must be html or latex, not {kind}")
 
         cmd = ["sphinx-build", "-b", kind]
         if self.num_jobs:
@@ -288,12 +288,6 @@ def zip_html(self):
         os.chdir(dirname)
         self._run_os("zip", zip_fname, "-r", "-q", *fnames)
 
-    def linkcheck(self):
-        """
-        Check for broken links in the documentation.
-        """
-        return self._sphinx_build("linkcheck")
-
 
 def main():
     cmds = [method for method in dir(DocBuilder) if not method.startswith("_")]
@@ -379,4 +373,4 @@ def main():
 
 
 if __name__ == "__main__":
-    sys.exit(main())
+    sys.exit(main())
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