A labyrinth seal is disclosed which reduces the inlet swirl and circumferential flow of fluid within the sealing cavity of a rotating shaft system. The primary purpose is to eliminate the destabilizing influence of the labyrinth seal which can induce rotor instability. This is accomplished by the addition of flow bypass passageways which extend from the high pressure face of the seal to the space between the first and second set of labyrinth teeth. The flow bypass passageways are equally spaced around the circumference of the seal and are inclined such that the fluid is introduced into the seal cavity at a desired orientation. Multiple sets of flow bypass passageways are also positioned at predetermined locations downstream from the first set of passages and function in a similar manner. Annular grooves are provided in the outer surface of the seal to connect each adjacent set of flow bypass passageways which straddle each set of labyrinth teeth.