For the Dirichlet problem on open arcs in an infinite plane, a modified numerical scheme using the indirect boundary integral method is presented. We suggest a single layer potential, added by a constant, as a solution of the problem. Then the solution for the density function of the induced boundary integral equation gives the potential which satisfies all the conditions of the original problem. Approximation to the unknown density function is fulfilled by using the collocation method with the Chebyshev polynomials of the first kind. The procedure given in this work reduces the number of steps for computation of the method introduced by Atkinson and Sloan . Experimental results of some examples are given to show the convergence of our method, which is the same as that of the literature .