diff --git a/crates/polars-core/src/chunked_array/logical/datetime.rs b/crates/polars-core/src/chunked_array/logical/datetime.rs
index 598e580dbe40..be53ccd19c93 100644
--- a/crates/polars-core/src/chunked_array/logical/datetime.rs
+++ b/crates/polars-core/src/chunked_array/logical/datetime.rs
@@ -80,23 +80,17 @@ impl LogicalType for DatetimeChunked {
                     .into_series()),
             },
             #[cfg(feature = "dtype-time")]
-            (Datetime(tu, _), Time) => match tu {
-                TimeUnit::Nanoseconds => Ok((self.0.as_ref() % NS_IN_DAY)
-                    .cast(&Int64)
-                    .unwrap()
+            (Datetime(tu, _), Time) => Ok({
+                let (modder, multiplier) = match tu {
+                    TimeUnit::Nanoseconds => (NS_IN_DAY, 1i64),
+                    TimeUnit::Microseconds => (US_IN_DAY, 1_000i64),
+                    TimeUnit::Milliseconds => (MS_IN_DAY, 1_000_000i64),
+                };
+                self.0
+                    .apply_values(|v| (v % modder * multiplier) + (NS_IN_DAY * (v < 0) as i64))
                     .into_time()
-                    .into_series()),
-                TimeUnit::Microseconds => Ok((self.0.as_ref() % US_IN_DAY * 1_000i64)
-                    .cast(&Int64)
-                    .unwrap()
-                    .into_time()
-                    .into_series()),
-                TimeUnit::Milliseconds => Ok((self.0.as_ref() % MS_IN_DAY * 1_000_000i64)
-                    .cast(&Int64)
-                    .unwrap()
-                    .into_time()
-                    .into_series()),
-            },
+                    .into_series()
+            }),
             _ => self.0.cast(dtype),
         }
     }
diff --git a/py-polars/tests/unit/namespaces/test_datetime.py b/py-polars/tests/unit/namespaces/test_datetime.py
index 20969441e298..66e0665a76d8 100644
--- a/py-polars/tests/unit/namespaces/test_datetime.py
+++ b/py-polars/tests/unit/namespaces/test_datetime.py
@@ -144,8 +144,18 @@ def test_local_datetime_sortedness(time_zone: str | None, expected: bool) -> Non
 def test_local_time_sortedness(time_zone: str | None) -> None:
     ser = (pl.Series([datetime(2022, 1, 1, 23)]).dt.replace_time_zone(time_zone)).sort()
     result = ser.dt.time()
-    assert result.flags["SORTED_ASC"] is False
-    assert result.flags["SORTED_DESC"] is False
+    assert result.flags["SORTED_ASC"]
+    assert not result.flags["SORTED_DESC"]
+
+
+@pytest.mark.parametrize("time_unit", ["ms", "us", "ns"])
+def test_local_time_before_epoch(time_unit: TimeUnit) -> None:
+    ser = pl.Series([datetime(1969, 7, 21, 2, 56, 2, 123000)]).dt.cast_time_unit(
+        time_unit
+    )
+    result = ser.dt.time().item()
+    expected = time(2, 56, 2, 123000)
+    assert result == expected
 
 
 @pytest.mark.parametrize(