The collisionless tearing mode in a neutral sheet is studied in the presence of ion temperature anisotropy using Vlasov description for both ions and electrons. It is found that the growth rate of the instability is significantly enhanced if Ti&ngr;>1 where the symbols I and II refer to the directions perpendicular and parallel to the equilibrium magnetic field. For typical magnetotail parameters with modest temperature anisotropy, it is shown that the linear e-folding time is reduced to a small fraction of the time delays believed to precede the onset of reconnection. This enhancement of the growth rate is due to the Lorentz force acting on the ions that cross the neutral plane, traversing beyond the conventional electron tearing layer.