The effect of noise on the reversal of a magnetic dipole is investigated on the basis of computer simulation of the Landau-Lifshits equation. It is demonstrated that at the reversal by the pulse with sinusoidal shape, there exists the optimal duration, which minimizes the mean reversal time (MRT) and the standard deviation (SD, jitter). Both the MRT and the jitter significantly depend on the angle between the reversal magnetic field and the anisotropy axis. At the optimal angle the MRT can be decreased by a factor of 7 for damping =1 and up to 2 orders of magnitude for =0.01, and the jitter can be decreased from 1 to 3 orders of magnitude in comparison with the uniaxial symmetry case. It has been demonstrated that fluctuations can not only decrease the reversal time, as it has been known before for the magnetic systems and is correct for small angles only, but it can also significantly, up to the factor of two, increase the reversal time.