  In this paper, we extend the inexact Uzawa algorithm in [Q. Hu, J. Zou, SIAM
J. Matrix Anal., 23(2001), pp. 317-338] to the nonsymmetric generalized saddle
point problem. The techniques used here are similar to those in [Bramble
\emph{et al}, Math. Comput. 69(1999), pp. 667-689], where the convergence of
Uzawa type algorithm for solving nonsymmetric case depends on the spectrum of
the preconditioners involved. The main contributions of this paper focus on a
new linear Uzawa type algorithm for nonsymmetric generalized saddle point
problems and its convergence. This new algorithm can always converge without
any prior estimate on the spectrum of two preconditioned subsystems involved,
which may not be easy to achieve in applications. Numerical results of the
algorithm on the Navier-Stokes problem are also presented.
