  Let $q$ be a positive integer, $\chi$ a nontrivial character mod $q$,
$\mathcal{I}$ an interval of length not exceeding $q.$ In this paper we shall
study the character sum analogue of the well-known Kloosterman
sum,\[\sum_{\substack{a\in\mathcal{I}
  \gcd(a,q)=1}}\chi(ma+n\overline{a}),\] where $\overline{a}$ is the
multiplicative inverse of $a\bmod q$. The mean square values and bilinear forms
for such sums are proved.
