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A descent Anderson-Moore method for solving the optimal constant output feedback gains for the stochastic discrete-time optimal output feedback problem is discussed. An efficient descent mapping algorithm is given in detail. The algorithm involves a partial line search mapping implemented as a finite search process to determine a step-length parameter so as to guarantee global convergence of the algorithm to a stationary point of the loss function under very mild assumptions. Furthermore, the algorithm involves a scheme to bound the condition numbers of certain critical matrix inverses in the Anderson-Moore method so that the algorithm can be applied to a wider class of control problems.