The preconditioned Arrow-Hurwicz-algorithm to solve the linear system \(Au+Bp=f\), \(B^ Tu=g\) is a modification of Uzawa’s algorithm, which was studied earlier by the author and U. Langer [J. Comput. Appl. Math. 15, 191-202 (1986; Zbl 0601.76021)]. The iteration parameters are chosen optimally. The convergence factor is estimated, in particular it is independent of the discretization parameter, if the system in question stems from certain mixed finite element problems. Some computational aspects are discussed. Finally, a general method to construct the preconditioning operators is given.