A new algorithm is presented for reduced-order modelling of linear discrete-time systems, using an output–error criterion. A closed form expression is developed for the gradient of the cost function with respect to the model parameters. A computationally efficient algorithm for computing this gradient is derived. A Fletcher — Powell optimization procedure utilizes the gradient vector to compute the reduced-order model parameters. A special initialization procedure is proposed, and the stability of the reduced – order system is monitored. The performance of the algorithm is illustrated by some numerical examples.