diff --git a/clang/lib/Sema/SemaDecl.cpp b/clang/lib/Sema/SemaDecl.cpp
--- a/clang/lib/Sema/SemaDecl.cpp
+++ b/clang/lib/Sema/SemaDecl.cpp
@@ -15108,10 +15108,12 @@
   }
 
   FunctionDecl *FD = nullptr;
+  bool IsFnTemplate = false;
 
-  if (FunctionTemplateDecl *FunTmpl = dyn_cast<FunctionTemplateDecl>(D))
+  if (FunctionTemplateDecl *FunTmpl = dyn_cast<FunctionTemplateDecl>(D)) {
     FD = FunTmpl->getTemplatedDecl();
-  else
+    IsFnTemplate = true;
+  } else
     FD = cast<FunctionDecl>(D);
 
   // Do not push if it is a lambda because one is already pushed when building
@@ -15260,7 +15262,7 @@
   // state is complete.
   if (getLangOpts().CPlusPlusModules && currentModuleIsHeaderUnit() &&
       FD->getFormalLinkage() == Linkage::ExternalLinkage &&
-      !FD->isInvalidDecl() && BodyKind != FnBodyKind::Delete &&
+      !FD->isInvalidDecl() && !IsFnTemplate && BodyKind != FnBodyKind::Delete &&
       BodyKind != FnBodyKind::Default && !FD->isInlined()) {
     assert(FD->isThisDeclarationADefinition());
     Diag(FD->getLocation(), diag::err_extern_def_in_header_unit);
diff --git a/clang/test/CXX/module/module.import/p6.cpp b/clang/test/CXX/module/module.import/p6.cpp
--- a/clang/test/CXX/module/module.import/p6.cpp
+++ b/clang/test/CXX/module/module.import/p6.cpp
@@ -22,6 +22,8 @@
 
 int bad_var_definition = 3;  // expected-error {{non-inline external definitions are not permitted in C++ header units}}
 
+/* The cases below should compile without diagnostics.  */
+
 class A {
 public:
     // This is a declaration instead of definition.
@@ -36,3 +38,10 @@
   S(S&);
 };
 S::S(S&) = default;
+
+template<class _Ep>
+int tmpl_OK (_Ep) { return 0; }
+
+template <class _T1>
+bool
+operator==(_T1& , _T1& ) { return false; }