The secure transmission of the simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) aided communication system is investigated. Considering the coupled phase shifts of STAR-RISs and the fair secrecy requirement of users, a novel secure beamforming design is proposed for addressing the unique full-space mutual eavesdropping of STAR-RIS aided communication. In particular, a penalty based secrecy beamforming algorithm is developed to solve the resulting non-convex optimization problem, where the closed-form solutions of the coupled transmission/reflection coefficients are obtained in each iteration. Numerical results demonstrate that 1) the proposed scheme achieves higher secrecy capacity than conventional RIS; 2) 4-bit discrete phase shifters are sufficient for secrecy guarantee.