diff --git a/llvm/lib/CodeGen/AsmPrinter/DIE.cpp b/llvm/lib/CodeGen/AsmPrinter/DIE.cpp
--- a/llvm/lib/CodeGen/AsmPrinter/DIE.cpp
+++ b/llvm/lib/CodeGen/AsmPrinter/DIE.cpp
@@ -198,6 +198,7 @@
   const DIE *p = this;
   while (p) {
     if (p->getTag() == dwarf::DW_TAG_compile_unit ||
+        p->getTag() == dwarf::DW_TAG_skeleton_unit ||
         p->getTag() == dwarf::DW_TAG_type_unit)
       return p;
     p = p->getParent();
diff --git a/llvm/test/DebugInfo/X86/fission-template.ll b/llvm/test/DebugInfo/X86/fission-template.ll
new file mode 100644
--- /dev/null
+++ b/llvm/test/DebugInfo/X86/fission-template.ll
@@ -0,0 +1,75 @@
+; Check that we handle template types for split-dwarf-inlining correctly.
+; RUN: llc -split-dwarf-file=%t.dwo -O2 < %s -dwarf-version=5 -mtriple=x86_64-unknown-linux-gnu -filetype=obj -o -  | llvm-dwarfdump - | FileCheck %s
+;
+; The test case is generated from the following code
+; clang -cc1 -emit-llvm -fdebug-info-for-profiling -fsplit-dwarf-inlining -debug-info-kind=constructor -dwarf-version=5 -split-dwarf-file temp.dwo -O2
+;
+; void f1();
+;
+; template <typename T>
+; void f2() {
+;   f1();
+; }
+;
+; void f3() {
+;   f2<int>();
+; }
+
+; CHECK:      .debug_info contents:
+; CHECK:        DW_TAG_skeleton_unit
+; CHECK:          DW_TAG_subprogram
+; CHECK-NEXT:     DW_AT_linkage_name	("_Z2f2IiEvv")
+; CHECK-NEXT:     DW_AT_name	("f2<int>")
+; CHECK:          DW_TAG_template_type_parameter
+; CHECK-NEXT:       DW_AT_type	(0x{{.*}} "int")
+; CHECK-NEXT:       DW_AT_name	("T")
+; CHECK:      .debug_info.dwo contents:
+; CHECK:        DW_TAG_compile_unit
+; CHECK:          DW_TAG_subprogram
+; CHECK-NEXT:     DW_AT_linkage_name	("_Z2f2IiEvv")
+; CHECK-NEXT:     DW_AT_name	("f2<int>")
+; CHECK:          DW_TAG_template_type_parameter
+; CHECK-NEXT:       DW_AT_type	(0x{{.*}} "int")
+; CHECK-NEXT:       DW_AT_name	("T")
+
+; ModuleID = 'split-debug-inlining-template.cpp'
+source_filename = "llvm-project/clang/test/CodeGen/split-debug-inlining-template.cpp"
+target datalayout = "e-m:e-p270:32:32-p271:32:32-p272:64:64-i64:64-f80:128-n8:16:32:64-S128"
+target triple = "x86_64-redhat-linux-gnu"
+
+; Function Attrs: mustprogress nounwind
+define dso_local void @_Z2f3v() local_unnamed_addr #0 !dbg !6 {
+entry:
+  tail call void @_Z2f1v() #2, !dbg !11
+  ret void, !dbg !17
+}
+
+declare !dbg !18 void @_Z2f1v() local_unnamed_addr #1
+
+attributes #0 = { mustprogress nounwind "frame-pointer"="none" "min-legal-vector-width"="0" "no-trapping-math"="true" "stack-protector-buffer-size"="8" "target-features"="+cx8,+mmx,+sse,+sse2,+x87" }
+attributes #1 = { "frame-pointer"="none" "no-trapping-math"="true" "stack-protector-buffer-size"="8" "target-features"="+cx8,+mmx,+sse,+sse2,+x87" }
+attributes #2 = { nounwind }
+
+!llvm.dbg.cu = !{!0}
+!llvm.module.flags = !{!2, !3, !4}
+!llvm.ident = !{!5}
+
+!0 = distinct !DICompileUnit(language: DW_LANG_C_plus_plus_14, file: !1, producer: "clang version 15.0.0 (https://github.com/llvm/llvm-project.git 8b2b9c3fa91ebe583f8c634482885a669b82a1f0)", isOptimized: true, runtimeVersion: 0, splitDebugFilename: "split-debug-inlining-template.c.tmp.dwo", emissionKind: FullDebug, debugInfoForProfiling: true, nameTableKind: None)
+!1 = !DIFile(filename: "llvm-project/clang/test/CodeGen/<stdin>", directory: "build-debug", checksumkind: CSK_MD5, checksum: "0fb39b3bb5a60928b5d9c251b2d91b2c")
+!2 = !{i32 7, !"Dwarf Version", i32 5}
+!3 = !{i32 2, !"Debug Info Version", i32 3}
+!4 = !{i32 1, !"wchar_size", i32 4}
+!5 = !{!"clang version 15.0.0 (https://github.com/llvm/llvm-project.git 8b2b9c3fa91ebe583f8c634482885a669b82a1f0)"}
+!6 = distinct !DISubprogram(name: "f3", linkageName: "_Z2f3v", scope: !7, file: !7, line: 11, type: !8, scopeLine: 11, flags: DIFlagPrototyped | DIFlagAllCallsDescribed, spFlags: DISPFlagDefinition | DISPFlagOptimized, unit: !0, retainedNodes: !10)
+!7 = !DIFile(filename: "llvm-project/clang/test/CodeGen/split-debug-inlining-template.cpp", directory: "", checksumkind: CSK_MD5, checksum: "0fb39b3bb5a60928b5d9c251b2d91b2c")
+!8 = !DISubroutineType(types: !9)
+!9 = !{null}
+!10 = !{}
+!11 = !DILocation(line: 8, column: 3, scope: !12, inlinedAt: !16)
+!12 = distinct !DISubprogram(name: "f2<int>", linkageName: "_Z2f2IiEvv", scope: !7, file: !7, line: 7, type: !8, scopeLine: 7, flags: DIFlagPrototyped | DIFlagAllCallsDescribed, spFlags: DISPFlagDefinition | DISPFlagOptimized, unit: !0, templateParams: !13, retainedNodes: !10)
+!13 = !{!14}
+!14 = !DITemplateTypeParameter(name: "T", type: !15)
+!15 = !DIBasicType(name: "int", size: 32, encoding: DW_ATE_signed)
+!16 = distinct !DILocation(line: 12, column: 3, scope: !6)
+!17 = !DILocation(line: 13, column: 1, scope: !6)
+!18 = !DISubprogram(name: "f1", linkageName: "_Z2f1v", scope: !7, file: !7, line: 4, type: !8, flags: DIFlagPrototyped, spFlags: DISPFlagOptimized, retainedNodes: !10)