diff --git a/Makefile.pre.in b/Makefile.pre.in
index 57167e61d39..2a687e58c91 100644
--- a/Makefile.pre.in
+++ b/Makefile.pre.in
@@ -586,11 +586,15 @@ pybuilddir.txt: $(BUILDPYTHON)
 		exit 1 ; \
 	fi
 
+# This is shared by the math and cmath modules
+Modules/_math.o: Modules/_math.c Modules/_math.h
+	$(CC) -c $(CCSHARED) $(PY_CORE_CFLAGS) -o $@ $<
+
 # Build the shared modules
 # Under GNU make, MAKEFLAGS are sorted and normalized; the 's' for
 # -s, --silent or --quiet is always the first char.
 # Under BSD make, MAKEFLAGS might be " -s -v x=y".
-sharedmods: $(BUILDPYTHON) pybuilddir.txt
+sharedmods: $(BUILDPYTHON) pybuilddir.txt Modules/_math.o
 	@case "$$MAKEFLAGS" in \
 	    *\ -s*|s*) quiet="-q";; \
 	    *) quiet="";; \
diff --git a/Misc/NEWS b/Misc/NEWS
index a182887f715..4532488a9f4 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -671,6 +671,10 @@ Build
 - Issue #24986: It is now possible to build Python on Windows without errors
   when external libraries are not available.
 
+- Issue #24421: Compile Modules/_math.c once, before building extensions.
+  Previously it could fail to compile properly if the math and cmath builds
+  were concurrent.
+
 - Issue #25798: Update OS X 10.5 installer to use OpenSSL 1.0.2e.
 
 Windows
diff --git a/setup.py b/setup.py
index da67731aa19..930b64a73ae 100644
--- a/setup.py
+++ b/setup.py
@@ -582,13 +582,17 @@ class PyBuildExt(build_ext):
 
         # array objects
         exts.append( Extension('array', ['arraymodule.c']) )
+
+        shared_math = 'Modules/_math.o'
         # complex math library functions
-        exts.append( Extension('cmath', ['cmathmodule.c', '_math.c'],
-                               depends=['_math.h'],
+        exts.append( Extension('cmath', ['cmathmodule.c'],
+                               extra_objects=[shared_math],
+                               depends=['_math.h', shared_math],
                                libraries=math_libs) )
         # math library functions, e.g. sin()
-        exts.append( Extension('math',  ['mathmodule.c', '_math.c'],
-                               depends=['_math.h'],
+        exts.append( Extension('math',  ['mathmodule.c'],
+                               extra_objects=[shared_math],
+                               depends=['_math.h', shared_math],
                                libraries=math_libs) )
 
         # time libraries: librt may be needed for clock_gettime()