Radial function interpolation of scattered data is a frequently used method for multivariate data fitting. One of the most frequently used radial functions is called shifted surface spline, introduced by Dyn, Levin and Rippa in [4] for �Then it is extended to �for �Many articles have studied its properties, as can be seen in [2, 3, 5, 14, 15, 18-21]. When dealing with this function, two frequently used error bounds were the one raised by Wu and Schaback in [17], and the one raised by Madych and Nelson in [12]. Both are �as �where l is a positive integer and d is the fill-distance. Then RBF people found that there should be a better error bound which was �as �where �was a constant. The reason was that this kind of radial function was smooth and every smooth function possessed an exponential-type error bound. However, the value of w was unknown and has been regarded as a hard question. This constant controls the convergence rate of the error bound and should be clarified. The purpose of this paper is to answer this question. In the meantime, we found that w highly depended on the shape parameter c contained in this radial function whose optimal choice was unknown and was a longstanding famous question.