The finite difference beam propagation method(FD-BPM)is very powerful and has been widely used for optical waveguide design. The precision of the method is decided by the order of Padé approximation and the step of calculation, which means higher order and smaller step will introduce smaller error, but the calculation time will be longer. For the purpose to obtain higher precision and shorter calculation time, some trial methods are used, and some new second order formulas expanded from the square root operator for BPM are got, and the numerical simulations show that the coefficients of those new second order formulas are more precise than that of the conventional one. Furthermore, the analysis also indicates that those trial methods can be applied to the higher order formulas for the FD-BPM.