diff --git a/src/lightning/pytorch/trainer/connectors/signal_connector.py b/src/lightning/pytorch/trainer/connectors/signal_connector.py
index 728d8b6b6ee43..be896c4b1f6a0 100644
--- a/src/lightning/pytorch/trainer/connectors/signal_connector.py
+++ b/src/lightning/pytorch/trainer/connectors/signal_connector.py
@@ -72,8 +72,10 @@ def _slurm_sigusr_handler_fn(self, signum: _SIGNUM, _: FrameType) -> None:
         for logger in self.trainer.loggers:
             logger.finalize("finished")
 
-        hpc_save_path = self.trainer._checkpoint_connector.hpc_save_path(self.trainer.default_root_dir)
-        self.trainer.save_checkpoint(hpc_save_path)
+        if self.trainer._checkpoint_connector._ckpt_path != "last":
+            log.info(f"Detecting SLURM environment and ckpt_path=='last'. Disabling hpc ckpt")
+            hpc_save_path = self.trainer._checkpoint_connector.hpc_save_path(self.trainer.default_root_dir)
+            self.trainer.save_checkpoint(hpc_save_path)
 
         if self.trainer.is_global_zero:
             # find job id
diff --git a/tests/tests_pytorch/trainer/connectors/test_signal_connector.py b/tests/tests_pytorch/trainer/connectors/test_signal_connector.py
index 8825db3727e86..aa7aa280eefa8 100644
--- a/tests/tests_pytorch/trainer/connectors/test_signal_connector.py
+++ b/tests/tests_pytorch/trainer/connectors/test_signal_connector.py
@@ -70,6 +70,20 @@ def training_step(self, batch, batch_idx):
     signal.signal(signal.SIGTERM, signal.SIG_DFL)
 
 
+@RunIf(skip_windows=True)
+@mock.patch("lightning.fabric.plugins.environments.slurm.SLURMEnvironment.detect", return_value=True)
+@mock.patch("lightning.pytorch.trainer.Trainer.save_checkpoint", mock.MagicMock())
+def test_hpc_ckpt_last_not_created(_, save_checkpoint, tmp_path):
+    """Test that when ckpt_path='last' hpc_ckpt is not created"""
+    model = BoringModel()
+    trainer = Trainer(default_root_dir=tmp_path, max_steps=1, logger=False)
+    trainer.fit(model, ckpt_path="last")    
+
+    connector = _SignalConnector(trainer)
+    connector._slurm_sigusr_handler_fn(None, None)
+    save_checkpoint.assert_not_called()
+
+
 @RunIf(skip_windows=True)
 @pytest.mark.parametrize("auto_requeue", [True, False])
 @pytest.mark.parametrize("requeue_signal", [signal.SIGUSR1, signal.SIGUSR2, signal.SIGHUP] if not _IS_WINDOWS else [])