The accuracy of wavelet approximation at resolution h = $2^{-k}$ to a smooth function f is limited by O($h^M$), where M is the number of vanishing moments of the mother wavelet ${psi}$; that is, the approximation order of wavelet approximation is M - 1. High accuracy points of wavelet approximation are of interest in some applications such as signal processing and numerical approximation. In this paper, we prove the scaling and translating properties of high accuracy points of wavelet approximation. To illustrate the results in this paper, we also present two examples of high accuracy points of wavelet approximation.