We investigate the possibility of appearance of new phenomena derived from the influence of noise on quantum systems. As a starting point we study the entanglement evolution of two coupled qubits in interaction with an external environment and in the presence of an external magnetic field with a stochastic component. The results show the expected degradation of entanglement due to the noise. The new effect is that for particular initial states the time of disentanglement depends in a non-monotonous way on the strength of the noise. We find that it is shortest for an intermediate strength value of the noise. This we call "stochastic anti-resonance." Our new result indicates that there are noise values which are particularly harmful and should be avoided. This could lead to a better understanding of noisy perturbations and their role for optimal designing of quantum devices.