diff --git a/flang/lib/Optimizer/HLFIR/Transforms/LowerHLFIRIntrinsics.cpp b/flang/lib/Optimizer/HLFIR/Transforms/LowerHLFIRIntrinsics.cpp
--- a/flang/lib/Optimizer/HLFIR/Transforms/LowerHLFIRIntrinsics.cpp
+++ b/flang/lib/Optimizer/HLFIR/Transforms/LowerHLFIRIntrinsics.cpp
@@ -1,4 +1,4 @@
-//===- LowerHLFIRIntrinsics.cpp - Bufferize HLFIR  ------------------------===//
+//===- LowerHLFIRIntrinsics.cpp - Transformational intrinsics to FIR ------===//
 //
 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
 // See https://llvm.org/LICENSE.txt for license information.
@@ -37,7 +37,22 @@
 /// runtime calls
 template <class OP>
 class HlfirIntrinsicConversion : public mlir::OpRewritePattern<OP> {
-  using mlir::OpRewritePattern<OP>::OpRewritePattern;
+public:
+  explicit HlfirIntrinsicConversion(mlir::MLIRContext *ctx)
+      : mlir::OpRewritePattern<OP>{ctx} {
+    // required for cases where intrinsics are chained together e.g.
+    // matmul(matmul(a, b), c)
+    // because converting the inner operation then invalidates the
+    // outer operation: causing the pattern to apply recursively.
+    //
+    // This is safe because we always progress with each iteration. Circular
+    // applications of operations are not expressible in MLIR because we use
+    // an SSA form and one must become first. E.g.
+    // %a = hlfir.matmul %b %d
+    // %b = hlfir.matmul %a %d
+    // cannot be written.
+    mlir::OpConversionPattern<OP>::setHasBoundedRewriteRecursion(true);
+  }
 
 protected:
   struct IntrinsicArgument {
diff --git a/flang/test/HLFIR/matmul-lowering.fir b/flang/test/HLFIR/matmul-lowering.fir
--- a/flang/test/HLFIR/matmul-lowering.fir
+++ b/flang/test/HLFIR/matmul-lowering.fir
@@ -43,3 +43,39 @@
 // CHECK:         hlfir.destroy %[[ASEXPR]]
 // CHECK-NEXT:    return
 // CHECK-NEXT:  }
+
+// nested matmuls leading to recursive pattern application
+func.func @_QPtest(%arg0: !fir.ref<!fir.array<3x3xf32>> {fir.bindc_name = "a"}, %arg1: !fir.ref<!fir.array<3x3xf32>> {fir.bindc_name = "b"}, %arg2: !fir.ref<!fir.array<3x3xf32>> {fir.bindc_name = "c"}, %arg3: !fir.ref<!fir.array<3x3xf32>> {fir.bindc_name = "out"}) {
+  %c3 = arith.constant 3 : index
+  %c3_0 = arith.constant 3 : index
+  %0 = fir.shape %c3, %c3_0 : (index, index) -> !fir.shape<2>
+  %1:2 = hlfir.declare %arg0(%0) {uniq_name = "_QFtestEa"} : (!fir.ref<!fir.array<3x3xf32>>, !fir.shape<2>) -> (!fir.ref<!fir.array<3x3xf32>>, !fir.ref<!fir.array<3x3xf32>>)
+  %c3_1 = arith.constant 3 : index
+  %c3_2 = arith.constant 3 : index
+  %2 = fir.shape %c3_1, %c3_2 : (index, index) -> !fir.shape<2>
+  %3:2 = hlfir.declare %arg1(%2) {uniq_name = "_QFtestEb"} : (!fir.ref<!fir.array<3x3xf32>>, !fir.shape<2>) -> (!fir.ref<!fir.array<3x3xf32>>, !fir.ref<!fir.array<3x3xf32>>)
+  %c3_3 = arith.constant 3 : index
+  %c3_4 = arith.constant 3 : index
+  %4 = fir.shape %c3_3, %c3_4 : (index, index) -> !fir.shape<2>
+  %5:2 = hlfir.declare %arg2(%4) {uniq_name = "_QFtestEc"} : (!fir.ref<!fir.array<3x3xf32>>, !fir.shape<2>) -> (!fir.ref<!fir.array<3x3xf32>>, !fir.ref<!fir.array<3x3xf32>>)
+  %c3_5 = arith.constant 3 : index
+  %c3_6 = arith.constant 3 : index
+  %6 = fir.shape %c3_5, %c3_6 : (index, index) -> !fir.shape<2>
+  %7:2 = hlfir.declare %arg3(%6) {uniq_name = "_QFtestEout"} : (!fir.ref<!fir.array<3x3xf32>>, !fir.shape<2>) -> (!fir.ref<!fir.array<3x3xf32>>, !fir.ref<!fir.array<3x3xf32>>)
+  %8 = hlfir.matmul %1#0 %3#0 {fastmath = #arith.fastmath<contract>} : (!fir.ref<!fir.array<3x3xf32>>, !fir.ref<!fir.array<3x3xf32>>) -> !hlfir.expr<3x3xf32>
+  %9 = hlfir.matmul %8 %5#0 {fastmath = #arith.fastmath<contract>} : (!hlfir.expr<3x3xf32>, !fir.ref<!fir.array<3x3xf32>>) -> !hlfir.expr<3x3xf32>
+  hlfir.assign %9 to %7#0 : !hlfir.expr<3x3xf32>, !fir.ref<!fir.array<3x3xf32>>
+  hlfir.destroy %9 : !hlfir.expr<3x3xf32>
+  hlfir.destroy %8 : !hlfir.expr<3x3xf32>
+  return
+}
+// just check that we apply the patterns successfully. The details are checked above
+// CHECK-LABEL: func.func @_QPtest(
+// CHECK:           %arg0: !fir.ref<!fir.array<3x3xf32>> {fir.bindc_name = "a"},
+// CHECK-SAME:      %arg1: !fir.ref<!fir.array<3x3xf32>> {fir.bindc_name = "b"},
+// CHECK-SAME:      %arg2: !fir.ref<!fir.array<3x3xf32>> {fir.bindc_name = "c"},
+// CHECK-SAME:      %arg3: !fir.ref<!fir.array<3x3xf32>> {fir.bindc_name = "out"}) {
+// CHECK:         fir.call @_FortranAMatmul(
+// CHECK;         fir.call @_FortranAMatmul(%40, %41, %42, %43, %c20_i32) : (!fir.ref<!fir.box<none>>, !fir.box<none>, !fir.box<none>, !fir.ref<i8>, i32) -> none
+// CHECK:         return
+// CHECK-NEXT:  }