diff --git a/flang/lib/Lower/ConvertType.cpp b/flang/lib/Lower/ConvertType.cpp
--- a/flang/lib/Lower/ConvertType.cpp
+++ b/flang/lib/Lower/ConvertType.cpp
@@ -75,6 +75,13 @@
   return {};
 }
 
+static mlir::Type genComplexType(mlir::MLIRContext *context, int KIND) {
+  if (Fortran::evaluate::IsValidKindOfIntrinsicType(
+          Fortran::common::TypeCategory::Complex, KIND))
+    return fir::ComplexType::get(context, KIND);
+  return {};
+}
+
 static mlir::Type genFIRType(mlir::MLIRContext *context,
                              Fortran::common::TypeCategory tc, int kind) {
   switch (tc) {
@@ -83,7 +90,7 @@
   case Fortran::common::TypeCategory::Integer:
     return genIntegerType(context, kind);
   case Fortran::common::TypeCategory::Complex:
-    TODO_NOLOC("genFIRType Complex");
+    return genComplexType(context, kind);
   case Fortran::common::TypeCategory::Logical:
     return genLogicalType(context, kind);
   case Fortran::common::TypeCategory::Character:
@@ -138,16 +145,6 @@
   return {};
 }
 
-template <>
-mlir::Type
-genFIRType<Fortran::common::TypeCategory::Complex>(mlir::MLIRContext *context,
-                                                   int KIND) {
-  if (Fortran::evaluate::IsValidKindOfIntrinsicType(
-          Fortran::common::TypeCategory::Complex, KIND))
-    return fir::ComplexType::get(context, KIND);
-  return {};
-}
-
 namespace {
 
 /// Discover the type of an Fortran::evaluate::Expr<T> and convert it to an
diff --git a/flang/test/Lower/basic-function.f90 b/flang/test/Lower/basic-function.f90
--- a/flang/test/Lower/basic-function.f90
+++ b/flang/test/Lower/basic-function.f90
@@ -98,3 +98,32 @@
 ! CHECK-LABEL: func @_QPrfct6() -> f128
 ! CHECK:         return %{{.*}} : f128
 
+complex(2) function cplxfct1()
+end
+! CHECK-LABEL: func @_QPcplxfct1() -> !fir.complex<2>
+! CHECK:         return %{{.*}} : !fir.complex<2>
+
+complex(3) function cplxfct2()
+end
+! CHECK-LABEL: func @_QPcplxfct2() -> !fir.complex<3>
+! CHECK:         return %{{.*}} : !fir.complex<3>
+
+complex(4) function cplxfct3()
+end
+! CHECK-LABEL: func @_QPcplxfct3() -> !fir.complex<4>
+! CHECK:         return %{{.*}} : !fir.complex<4>
+
+complex(8) function cplxfct4()
+end
+! CHECK-LABEL: func @_QPcplxfct4() -> !fir.complex<8>
+! CHECK:         return %{{.*}} : !fir.complex<8>
+
+complex(10) function cplxfct5()
+end
+! CHECK-LABEL: func @_QPcplxfct5() -> !fir.complex<10>
+! CHECK:         return %{{.*}} : !fir.complex<10>
+
+complex(16) function cplxfct6()
+end
+! CHECK-LABEL: func @_QPcplxfct6() -> !fir.complex<16>
+! CHECK:         return %{{.*}} : !fir.complex<16>