diff --git a/Makefile.pre.in b/Makefile.pre.in
index 3312c6f36e2..8d7f5ad7916 100644
--- a/Makefile.pre.in
+++ b/Makefile.pre.in
@@ -1101,7 +1101,7 @@ sharedinstall: sharedmods
 	   	--prefix=$(prefix) \
 		--install-scripts=$(BINDIR) \
 		--install-platlib=$(DESTSHARED) \
-		--root=/$(DESTDIR)
+		--root=$(DESTDIR)/
 
 # Here are a couple of targets for MacOSX again, to install a full
 # framework-based Python. frameworkinstall installs everything, the
@@ -1172,7 +1172,7 @@ scriptsinstall:
 	./$(BUILDPYTHON) $(srcdir)/Tools/scripts/setup.py install \
 	--prefix=$(prefix) \
 	--install-scripts=$(BINDIR) \
-	--root=/$(DESTDIR)
+	--root=$(DESTDIR)/
 
 # Build the toplevel Makefile
 Makefile.pre: Makefile.pre.in config.status
diff --git a/Misc/NEWS b/Misc/NEWS
index 0f741448f24..41c5edc9077 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -154,6 +154,8 @@ Library
 Build
 -----
 
+- Issue #11411: Fix 'make DESTDIR=' with a relative destination.
+
 - Issue #11268: Prevent Mac OS X Installer failure if Documentation
   package had previously been installed.