The present paper is concerned with the frictionless bilateral or unilateral contact problem between two elastic bodies. An algorithm is introduced to solve the resulting finite element system by a non-overlapping domain decomposition method. This technique enable us to transform the solution of the global problem to the solutions of the elasticity equations for each body separately and the solution of the Schur complement problem on the contact surface. The main goal of this work is the construction of the interface preconditioner for the Schur complement problem. The solution is obtained by using a successive approximation method. Finally, some numerical results of the proposed method are given. © 2008 American Institute of Physics.