diff --git a/Makefile.pre.in b/Makefile.pre.in
index d385db2a340..2b28cae902f 100644
--- a/Makefile.pre.in
+++ b/Makefile.pre.in
@@ -1059,7 +1059,7 @@ 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
@@ -1131,7 +1131,7 @@ 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 3e5cd8ece09..d562026ff88 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -207,6 +207,8 @@ Extension Modules
 Build
 -----
 
+- Issue #11411: Fix 'make DESTDIR=' with a relative destination.
+
 - Issue #10709: Add updated AIX notes in Misc/README.AIX.
 
 - Issue #11184: Fix large-file support on AIX.