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Multivariable bilinear state-space systems can be identified by optimizing an output-error cost function. In this paper a full parameterization of the bilinear system is used. An iterative local gradient search method is used to solve the nonlinear optimization problem. It takes care of the nonuniqueness of the fully parameterized state-space model by restricting the update of the parameters to directions that change the input-output behavior of the model. Colored noise at the output of the bilinear system can be taken into account by a suitable weighting of the cost function; it results in a maximum likelihood identification procedure.