diff --git a/ProcessorTargets.cmake b/ProcessorTargets.cmake
index aa06b29ee..a752dceeb 100644
--- a/ProcessorTargets.cmake
+++ b/ProcessorTargets.cmake
@@ -6,7 +6,18 @@ set(PROC_TARGET_1_FLAGS "-mtune=generic" CACHE STRING "Processor-1 flags")
 
 # This second choice should be used for your own build only
 set(PROC_TARGET_2_LABEL native CACHE STRING "Processor-2 label - use it for your own build")
-set(PROC_TARGET_2_FLAGS "-march=native" CACHE STRING "Processor-2 flags")
+
+# Get the architecture on an Apple system (x86 or arm64)
+if(APPLE)
+    execute_process(COMMAND uname -m OUTPUT_VARIABLE APPLE_ARCHITECTURE OUTPUT_STRIP_TRAILING_WHITESPACE)
+endif()
+
+# On Apple's M1 processor and with Apple's clang compiler, the native flag is different
+if(CMAKE_CXX_COMPILER_ID STREQUAL AppleClang AND APPLE_ARCHITECTURE STREQUAL arm64)
+    set(PROC_TARGET_2_FLAGS "-mcpu=native" CACHE STRING "Processor-2 flags")
+else()
+    set(PROC_TARGET_2_FLAGS "-march=native" CACHE STRING "Processor-2 flags")
+endif()
 
 # The later choices is intended to be used if you want to provide specific builds, but it should match your own processor
 # You can cross compile but you have to know what you're doing, this mechanism has not been designed for that