  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
\cite{Dy1} for $R^{2}$. Then it's extended to $R^{n}$ for $n\geq 1$. Many
articles have studied its properties, as can be seen in
\cite{Bu,Du,Dy2,Po,Ri,Yo1,Yo2,Yo3,Yo4}. When dealing with this function, the
most commonly used error bounds are the one raised by Wu and Schaback in
\cite{WS}, and the one raised by Madych and Nelson in \cite{MN2}. Both are
$O(d^{l})$ as $d\to 0$, where $l$ is a positive integer and $d$ is the
fill-distance. In this paper we present an improved error bound which is
$O(\omega^{1/d})$ as $d\to 0$, where $0<\omega <1$ is a constant which can be
accurately calculated.
