We construct an orthonormal basis for the Bergman space associated to a simply connected domain. We use the orthonormal basis for the Hardy space consisting of the Szeg\H o kernel and the Riemann mapping function and rewrite their area integrals in terms of arc length integrals using the complex Green''s identity. And we make a note about the matrix of a Toeplitz operator with respect to the orthonormal basis constructed in the paper.