We show in the paper that the decomposition proposed by Beveridge and Nelson (1981) for models that are integrated of order one can be generalized to seasonal Arima models by means of a partial fraction decomposition. Two equivalent algorithms are proposed to optimally (in the mean squared sense) compute the estimates of the components in the generalized decomposition. While the first algorithm is very fast and easy to implement, the second can also provide the standard errors of the estimated components. The properties of the implied filters are investigated and compared with those obtained using the model-based TRAMO/SEATS software package. The alternative methods are applied to the German unemployment series.