diff --git a/hooks/conan-center.py b/hooks/conan-center.py
index b0b7b52f..42ef11a6 100644
--- a/hooks/conan-center.py
+++ b/hooks/conan-center.py
@@ -984,6 +984,7 @@ def test(out):
                       "be located using generators and the declared `cpp_info` information")
             out.error("Found files: {}".format("; ".join(bad_files)))
 
+
     @run_test("KB-H016", output)
     def test(out):
         if conanfile.name in ["cmake", "msys2", "strawberryperl", "pybind11", "ignition-cmake",
@@ -1034,6 +1035,33 @@ def post_package_info(output, conanfile, reference, **kwargs):
     if not hasattr(this, "reference") or str(reference) != this.reference:
         return
 
+    @run_test("KB-H016", output)
+    def test(out):
+        if conanfile.name in ["cmake", "msys2", "strawberryperl"]:
+            return
+        bad_files = _get_files_following_patterns(conanfile.package_folder, ["Find*.cmake",
+                                                                             "*Config.cmake",
+                                                                             "*-config.cmake"])
+
+        target = "find{}.cmake".format(conanfile.name.lower())
+        try:
+            target = "find{}.cmake".format(conanfile.cpp_info.names["cmake_find_package"].lower())
+        except:
+            pass
+
+        for bad_file in bad_files:
+            bad_file_name = os.path.basename(bad_file).lower()
+            if bad_file_name.startswith("find") and bad_file_name.endswith(
+                    ".cmake") and bad_file_name != target:
+                bad_files.remove(bad_file)
+                break
+
+        if bad_files:
+            out.error("The conan-center repository doesn't allow the packages to contain CMake "
+                      "find modules or config files. The packages have to "
+                      "be located using generators and the declared `cpp_info` information")
+            out.error("Found files:\n{}".format("\n".join(bad_files)))
+
     @run_test("KB-H019", output)
     def test(out):
         if conanfile.name in ["android-ndk", "cmake", "msys2", "strawberryperl"]:
diff --git a/tests/test_hooks/conan-center/test_cmake_bad_files.py b/tests/test_hooks/conan-center/test_cmake_bad_files.py
index 5c323eed..e77ae21c 100644
--- a/tests/test_hooks/conan-center/test_cmake_bad_files.py
+++ b/tests/test_hooks/conan-center/test_cmake_bad_files.py
@@ -49,6 +49,9 @@ def test_find_and_config_files(self):
     def test_find_and_find_files(self):
         tools.save('conanfile.py', content=self.conan_file.format("", "FindXXX.cmake"))
         output = self.conan(['create', '.', 'name/version@user/channel'])
+
+        self.assertNotIn("ERROR: [CMAKE-MODULES-CONFIG-FILES (KB-H016)]", output)
+
         self.assertIn("ERROR: [CMAKE-MODULES-CONFIG-FILES (KB-H016)] Found files: ./FindXXX.cmake",
                       output)
 
@@ -126,3 +129,24 @@ def package_info(self):
         tools.save('conanfile.py', content=conanfile)
         output = self.conan(['create', '.', 'name/version@user/channel'])
         self.assertNotIn("ERROR: [CMAKE FILE NOT IN BUILD FOLDERS (KB-H019)]", output)
+
+    def test_find_package_names(self):
+        tools.save('conanfile.py', content=self.conan_file.format("lib/foo/cmake", "FindFoo.cmake"))
+        output = self.conan(['create', '.', 'foo/version@user/channel'])
+        self.assertIn("ERROR: [CMAKE-MODULES-CONFIG-FILES (KB-H016)] Found files:\n./lib/foo/cmake/FindFoo.cmake",
+                      output)
+
+        conan_file3 = textwrap.dedent("""\
+                        import os
+                        from conans import ConanFile, tools
+                        class AConan(ConanFile):
+                            def package(self):
+                                tools.save(os.path.join(self.package_folder, "lib", "foo", "cmake", "FindBar.cmake"), "foo")
+
+                            def package_info(self):
+                                self.cpp_info.names["cmake_find_package"] = "Bar"
+                        """)
+        tools.save('conanfile.py', conan_file3)
+        output = self.conan(['create', '.', 'foo/version@user/channel'])
+        self.assertIn("ERROR: [CMAKE-MODULES-CONFIG-FILES (KB-H016)] Found files:\n./lib/foo/cmake/FindBar.cmake",
+                      output)
\ No newline at end of file