This paper deals with the stability of the second order difference equation possessing periodic parameter, which characterizes discrete periodic system. Discrete periodic system corresponding to Mathieu equation is expressed as second order difference equation with small parameter ε in the time-varying term. This parameter ε plays an important role in stability. For the fundamental equation without damping, stability boundary curves are analytically obtained with respect to parameters in the equation by using McLachlan's method, which is based on Floquet's theory and perturbation method. The boundary curves are computed by pursuing periodic solutions on the boundaries and letting secular term zero. The boundary curves are expressed as the power series of ε. When periodic parameter consists of even function of Fourier series, stability boundary curves are obtained. For the fundamental equation with damping, stability criterion is shown in the neighbor of important resonant points. This criterion is obtained by computing points on the boundary curves.