diff --git a/flang/runtime/extrema.cpp b/flang/runtime/extrema.cpp
--- a/flang/runtime/extrema.cpp
+++ b/flang/runtime/extrema.cpp
@@ -60,8 +60,10 @@
 template <typename COMPARE> class ExtremumLocAccumulator {
 public:
   using Type = typename COMPARE::Type;
-  ExtremumLocAccumulator(const Descriptor &array, std::size_t chars = 0)
-      : array_{array}, argRank_{array.rank()}, compare_{array.ElementBytes()} {
+  ExtremumLocAccumulator(
+      const Descriptor &array, const Descriptor *mask = nullptr)
+      : array_{array}, argRank_{array.rank()}, compare_{array.ElementBytes()},
+        mask_(mask) {
     Reinitialize();
   }
   void Reinitialize() {
@@ -77,8 +79,15 @@
       *p = extremumLoc_[zeroBasedDim] -
           array_.GetDimension(zeroBasedDim).LowerBound() + 1;
     } else {
-      for (int j{0}; j < argRank_; ++j) {
-        p[j] = extremumLoc_[j] - array_.GetDimension(j).LowerBound() + 1;
+      // Either mask is missing or it's scalar .FALSE.
+      if (mask_) {
+        // Scalar .FALSE. -- all values are zero
+        *p = 0;
+      } else {
+        // No mask
+        for (int j{0}; j < argRank_; ++j) {
+          p[j] = extremumLoc_[j] - array_.GetDimension(j).LowerBound() + 1;
+        }
       }
     }
   }
@@ -99,6 +108,7 @@
   SubscriptValue extremumLoc_[maxRank];
   const Type *previous_{nullptr};
   COMPARE compare_;
+  const Descriptor *mask_;
 };
 
 template <typename ACCUMULATOR, typename CPPTYPE>
@@ -200,7 +210,7 @@
     const Descriptor *mask, Terminator &terminator) {
   using CppType = CppTypeFor<CAT, KIND>;
   using Accumulator = ExtremumLocAccumulator<COMPARE<CppType, IS_MAX, BACK>>;
-  Accumulator accumulator{x};
+  Accumulator accumulator{x, mask};
   ApplyIntegerKind<PartialLocationHelper<Accumulator>::template Functor, void>(
       kind, terminator, result, x, dim, mask, terminator, intrinsic,
       accumulator);
diff --git a/flang/unittests/Runtime/Reduction.cpp b/flang/unittests/Runtime/Reduction.cpp
--- a/flang/unittests/Runtime/Reduction.cpp
+++ b/flang/unittests/Runtime/Reduction.cpp
@@ -158,12 +158,84 @@
   EXPECT_EQ(scalarResult.rank(), 0);
   EXPECT_EQ(*scalarResult.ZeroBasedIndexedElement<std::int16_t>(0), 23);
   scalarResult.Destroy();
+
+  // Test .FALSE. scalar MASK argument
+  auto falseMask{MakeArray<TypeCategory::Logical, 4>(
+      std::vector<int>{}, std::vector<std::int32_t>{0})};
+  RTNAME(MaxlocDim)
+  (loc, *array, /*KIND=*/4, /*DIM=*/2, __FILE__, __LINE__,
+      /*MASK=*/&*falseMask, /*BACK=*/false);
+  EXPECT_EQ(loc.rank(), 2);
+  EXPECT_EQ(loc.type().raw(), (TypeCode{TypeCategory::Integer, 4}.raw()));
+  EXPECT_EQ(loc.GetDimension(0).LowerBound(), 1);
+  EXPECT_EQ(loc.GetDimension(0).Extent(), 3);
+  EXPECT_EQ(loc.GetDimension(1).LowerBound(), 1);
+  EXPECT_EQ(loc.GetDimension(1).Extent(), 2);
+  for (int i{0}; i < 6; ++i) {
+    EXPECT_EQ(*loc.ZeroBasedIndexedElement<std::int32_t>(0), 0);
+  }
+  loc.Destroy();
+
+  // Test .TRUE. scalar MASK argument
+  auto trueMask{MakeArray<TypeCategory::Logical, 4>(
+      std::vector<int>{}, std::vector<std::int32_t>{1})};
+  RTNAME(MaxlocDim)
+  (loc, *array, /*KIND=*/4, /*DIM=*/2, __FILE__, __LINE__,
+      /*MASK=*/&*trueMask, /*BACK=*/false);
+  EXPECT_EQ(loc.rank(), 2);
+  EXPECT_EQ(loc.type().raw(), (TypeCode{TypeCategory::Integer, 4}.raw()));
+  EXPECT_EQ(loc.GetDimension(0).LowerBound(), 1);
+  EXPECT_EQ(loc.GetDimension(0).Extent(), 3);
+  EXPECT_EQ(loc.GetDimension(1).LowerBound(), 1);
+  EXPECT_EQ(loc.GetDimension(1).Extent(), 2);
+  EXPECT_EQ(*loc.ZeroBasedIndexedElement<std::int32_t>(0), 3);
+  EXPECT_EQ(*loc.ZeroBasedIndexedElement<std::int32_t>(1), 4);
+  EXPECT_EQ(*loc.ZeroBasedIndexedElement<std::int32_t>(2), 3);
+  EXPECT_EQ(*loc.ZeroBasedIndexedElement<std::int32_t>(3), 3);
+  EXPECT_EQ(*loc.ZeroBasedIndexedElement<std::int32_t>(4), 4);
+  EXPECT_EQ(*loc.ZeroBasedIndexedElement<std::int32_t>(5), 4);
+  loc.Destroy();
+
   RTNAME(MinlocDim)
   (scalarResult, *array1, /*KIND=*/2, /*DIM=*/1, __FILE__, __LINE__,
       /*MASK=*/nullptr, /*BACK=*/true);
   EXPECT_EQ(scalarResult.rank(), 0);
   EXPECT_EQ(*scalarResult.ZeroBasedIndexedElement<std::int16_t>(0), 22);
   scalarResult.Destroy();
+
+  // Test .FALSE. scalar MASK argument
+  RTNAME(MinlocDim)
+  (loc, *array, /*KIND=*/4, /*DIM=*/2, __FILE__, __LINE__,
+      /*MASK=*/&*falseMask, /*BACK=*/false);
+  EXPECT_EQ(loc.rank(), 2);
+  EXPECT_EQ(loc.type().raw(), (TypeCode{TypeCategory::Integer, 4}.raw()));
+  EXPECT_EQ(loc.GetDimension(0).LowerBound(), 1);
+  EXPECT_EQ(loc.GetDimension(0).Extent(), 3);
+  EXPECT_EQ(loc.GetDimension(1).LowerBound(), 1);
+  EXPECT_EQ(loc.GetDimension(1).Extent(), 2);
+  for (int i{0}; i < 6; ++i) {
+    EXPECT_EQ(*loc.ZeroBasedIndexedElement<std::int32_t>(0), 0);
+  }
+  loc.Destroy();
+
+  // Test .TRUE. scalar MASK argument
+  RTNAME(MinlocDim)
+  (loc, *array, /*KIND=*/4, /*DIM=*/2, __FILE__, __LINE__,
+      /*MASK=*/&*trueMask, /*BACK=*/false);
+  EXPECT_EQ(loc.rank(), 2);
+  EXPECT_EQ(loc.type().raw(), (TypeCode{TypeCategory::Integer, 4}.raw()));
+  EXPECT_EQ(loc.GetDimension(0).LowerBound(), 1);
+  EXPECT_EQ(loc.GetDimension(0).Extent(), 3);
+  EXPECT_EQ(loc.GetDimension(1).LowerBound(), 1);
+  EXPECT_EQ(loc.GetDimension(1).Extent(), 2);
+  EXPECT_EQ(*loc.ZeroBasedIndexedElement<std::int32_t>(0), 4);
+  EXPECT_EQ(*loc.ZeroBasedIndexedElement<std::int32_t>(1), 3);
+  EXPECT_EQ(*loc.ZeroBasedIndexedElement<std::int32_t>(2), 4);
+  EXPECT_EQ(*loc.ZeroBasedIndexedElement<std::int32_t>(3), 4);
+  EXPECT_EQ(*loc.ZeroBasedIndexedElement<std::int32_t>(4), 3);
+  EXPECT_EQ(*loc.ZeroBasedIndexedElement<std::int32_t>(5), 2);
+  loc.Destroy();
+
   RTNAME(MaxvalDim)
   (scalarResult, *array1, /*DIM=*/1, __FILE__, __LINE__, /*MASK=*/nullptr);
   EXPECT_EQ(scalarResult.rank(), 0);