diff --git a/gdb/corelow.c b/gdb/corelow.c
index 8c33fb7ebb2..2037ef3dc89 100644
--- a/gdb/corelow.c
+++ b/gdb/corelow.c
@@ -122,6 +122,9 @@ public:
 
 private: /* per-core data */
 
+  /* Get rid of the core inferior.  */
+  void clear_core ();
+
   /* The core's section table.  Note that these target sections are
      *not* mapped in the current address spaces' set of target
      sections --- those should come only from pure executable or
@@ -308,10 +311,8 @@ core_target::build_file_mappings ()
 /* An arbitrary identifier for the core inferior.  */
 #define CORELOW_PID 1
 
-/* Close the core target.  */
-
 void
-core_target::close ()
+core_target::clear_core ()
 {
   if (core_bfd)
     {
@@ -325,6 +326,14 @@ core_target::close ()
 
       current_program_space->cbfd.reset (nullptr);
     }
+}
+
+/* Close the core target.  */
+
+void
+core_target::close ()
+{
+  clear_core ();
 
   /* Core targets are heap-allocated (see core_target_open), so here
      we delete ourselves.  */
@@ -631,9 +640,15 @@ core_target_open (const char *arg, int from_tty)
 void
 core_target::detach (inferior *inf, int from_tty)
 {
-  /* Note that 'this' is dangling after this call.  unpush_target
-     closes the target, and our close implementation deletes
-     'this'.  */
+  /* Get rid of the core.  Don't rely on core_target::close doing it,
+     because target_detach may be called with core_target's refcount > 1,
+     meaning core_target::close may not be called yet by the
+     unpush_target call below.  */
+  clear_core ();
+
+  /* Note that 'this' may be dangling after this call.  unpush_target
+     closes the target if the refcount reaches 0, and our close
+     implementation deletes 'this'.  */
   inf->unpush_target (this);
 
   /* Clear the register cache and the frame cache.  */
diff --git a/gdb/testsuite/gdb.base/corefile.exp b/gdb/testsuite/gdb.base/corefile.exp
index fa9d8243a59..0bb808d38b5 100644
--- a/gdb/testsuite/gdb.base/corefile.exp
+++ b/gdb/testsuite/gdb.base/corefile.exp
@@ -201,6 +201,16 @@ gdb_test "up" "#\[0-9\]* *\[0-9xa-fH'\]* in .* \\(.*\\).*" "up in corefile.exp (
 
 gdb_test "core" "No core file now."
 
+# Test that we can unload the core with the "detach" command.
+
+proc_with_prefix corefile_detach {} {
+    clean_restart $::binfile
+
+    gdb_test "core-file $::corefile" "Core was generated by .*" "load core"
+    gdb_test "detach" "No core file now\\." "detach core"
+}
+
+corefile_detach
 
 # Test a run (start) command will clear any loaded core file.
 
@@ -216,6 +226,8 @@ proc corefile_test_run {} {
 	return
     }
 
+    clean_restart $::binfile
+
     gdb_test "core-file $corefile" "Core was generated by .*" "run: load core again"
     gdb_test "info files" "\r\nLocal core dump file:\r\n.*" "run: sanity check we see the core file"