In this paper we propose an accurate approximation for the Bit Error Probability (BEP) for the case of four-phase differential phase shift keying (4-DPSK). The BER can be expressed in terms of the first order Marcum Q-function, which have no closed form. By approximating the modified Bessel function and the integrand of the Marcum Q-function with a polynomial function, new simple approximate expression for the BER can be derived. Comparison with existing approximations shows that our new estimator can provide more accurate results.