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This paper discusses a class of nonlinear second order discrete boundary value problems with parameter. We obtain the multiplicity result of symmetric solution for the problem in the condition that the nonlinear term grows in sublinear state. We determine different number of symmetric solutions of the problem in different range of the parameter near the resonant point, and each of theses solutions has its specific parity. The main methods used in this paper include Leray-Schauder principle and bifurcation theorem.