We shall consider the selfadjoint singularly perturbed problem described by the second order diferrential equation. The solution inside the layer is approximated by Newton’s iteration represented in the form of truncated orthogonal series due to the Chebyshev basis. For that purpose, the domain decomposition is performed according to the suitable resemblance function. The coefficients of the spectral approximation are determined by the collocation method at Gauss-Lobatto nodes. The error function is estimated according to the principle of inverse monotonicity, using the asymptotic behavior of the exact solution. Numerical results show high accuracy of the presented method.