In this paper we construct an orthogonal trigonometric Schauder basis in the space C(T2) which has a small growth of the polynomial degree. The polynomial degree is considered in terms of the ℓ1- and ℓ∞-norm. To construct this basis we use a dyadic anisotropic periodic multiresolution analysis and corresponding wavelet spaces. The multiresolution analysis is formed using the sequence of only rotation matrices. The focus of attention is the estimation of the norm of the corresponding orthogonal projection operator.