diff --git a/flang/lib/Optimizer/Transforms/CUFAddConstructor.cpp b/flang/lib/Optimizer/Transforms/CUFAddConstructor.cpp
index dd204126be5db..73a46843f0320 100644
--- a/flang/lib/Optimizer/Transforms/CUFAddConstructor.cpp
+++ b/flang/lib/Optimizer/Transforms/CUFAddConstructor.cpp
@@ -106,8 +106,7 @@ struct CUFAddConstructor
 
         mlir::func::FuncOp func;
         switch (attr.getValue()) {
-        case cuf::DataAttribute::Device:
-        case cuf::DataAttribute::Constant: {
+        case cuf::DataAttribute::Device: {
           func = fir::runtime::getRuntimeFunc<mkRTKey(CUFRegisterVariable)>(
               loc, builder);
           auto fTy = func.getFunctionType();
@@ -145,8 +144,6 @@ struct CUFAddConstructor
         default:
           break;
         }
-        if (!func)
-          continue;
       }
     }
     builder.create<mlir::LLVM::ReturnOp>(loc, mlir::ValueRange{});
diff --git a/flang/test/Fir/CUDA/cuda-constructor-2.f90 b/flang/test/Fir/CUDA/cuda-constructor-2.f90
index 901497e2cde55..29efdb083878a 100644
--- a/flang/test/Fir/CUDA/cuda-constructor-2.f90
+++ b/flang/test/Fir/CUDA/cuda-constructor-2.f90
@@ -30,3 +30,33 @@ module attributes {dlti.dl_spec = #dlti.dl_spec<#dlti.dl_entry<!llvm.ptr, dense<
 // CHECK-DAG: %[[BOXREF:.*]] = fir.convert %[[BOX]] : (!fir.ref<!fir.box<!fir.heap<!fir.array<?xi32>>>>) -> !fir.ref<i8>
 // CHECK-DAG: fir.call @_FortranACUFRegisterVariable(%[[MODULE:.*]], %[[BOXREF]], %{{.*}}, %{{.*}}) 
 //
+
+// ----- 
+
+// Checking that constant global variables are not registered
+
+// CHECK: @_FortranACUFRegisterAllocator
+// CHECK-NOT: fir.call @_FortranACUFRegisterVariable
+
+module attributes {dlti.dl_spec = #dlti.dl_spec<i8 = dense<8> : vector<2xi64>, i16 = dense<16> : vector<2xi64>, i1 = dense<8> : vector<2xi64>, !llvm.ptr = dense<64> : vector<4xi64>, f80 = dense<128> : vector<2xi64>, i128 = dense<128> : vector<2xi64>, i64 = dense<64> : vector<2xi64>, !llvm.ptr<271> = dense<32> : vector<4xi64>, !llvm.ptr<272> = dense<64> : vector<4xi64>, f128 = dense<128> : vector<2xi64>, !llvm.ptr<270> = dense<32> : vector<4xi64>, f16 = dense<16> : vector<2xi64>, f64 = dense<64> : vector<2xi64>, i32 = dense<32> : vector<2xi64>, "dlti.stack_alignment" = 128 : i64, "dlti.endianness" = "little">, fir.defaultkind = "a1c4d8i4l4r4", fir.kindmap = "", gpu.container_module, llvm.data_layout = "e-m:e-p270:32:32-p271:32:32-p272:64:64-i64:64-i128:128-f80:128-n8:16:32:64-S128", llvm.ident = "flang version 20.0.0 (https://github.com/llvm/llvm-project.git 3372303188df0f7f8ac26e7ab610cf8b0f716d42)", llvm.target_triple = "x86_64-unknown-linux-gnu"} {
+  fir.global @_QMiso_c_bindingECc_int {data_attr = #cuf.cuda<constant>} constant : i32
+  
+
+  fir.type_info @_QM__fortran_builtinsT__builtin_c_ptr noinit nodestroy nofinal : !fir.type<_QM__fortran_builtinsT__builtin_c_ptr{__address:i64}>
+  gpu.module @cuda_device_mod {
+    fir.global @_QMiso_c_bindingECc_int {data_attr = #cuf.cuda<constant>} constant : i32
+    gpu.func @_QMdevmodPdevsub(%arg0: !fir.ref<!fir.box<!fir.heap<!fir.array<?xf32>>>>) -> i32 {
+      %c0 = arith.constant 0 : index
+      %c4_i32 = arith.constant 4 : i32
+      %0 = fir.alloca i32 {bindc_name = "devsub", uniq_name = "_QMdevmodFdevsubEdevsub"}
+      %1 = fir.alloca i32 {bindc_name = "__builtin_warpsize", uniq_name = "_QM__fortran_builtinsEC__builtin_warpsize"}
+      %2 = fir.load %arg0 : !fir.ref<!fir.box<!fir.heap<!fir.array<?xf32>>>>
+      %3:3 = fir.box_dims %2, %c0 : (!fir.box<!fir.heap<!fir.array<?xf32>>>, index) -> (index, index, index)
+      %4 = fir.convert %3#1 : (index) -> i32
+      %5 = arith.muli %4, %c4_i32 : i32
+      fir.store %5 to %0 : !fir.ref<i32>
+      %6 = fir.load %0 : !fir.ref<i32>
+      gpu.return %6 : i32
+    }
+  }
+}
\ No newline at end of file