In network coding, information transmission often encounters wiretapping attacks. Secure network coding is introduced to prevent information from being leaked to adversaries. For secure linear network codes (SLNCs), the required field size is a very important index, because it largely determines the computational and space complexities of a SLNC, and it is also very important for the process of secure network coding from theoretical research to practical application. In this letter, we further discuss the required field size of SLNCs, and obtain a new lower bound. This bound shows that the field size of SLNCs can be reduced further, and much smaller than the known results for almost all cases.