It is well known that the determinant ratio of the product moment matrix of observed input/output data gives a quick way of testing the order of a linear discrete system, and that the IPM (instrumental product moment) matrix is useful for eliminating the effect of the noise. This paper describes the dimensionally recursive algorithm for the determinant ratio associated with a new IPM matrix. This IPM matrix is constructed by using the lagged inputs themselves as the instrumental variables so that it would have a nesting structure. The algorithm is derived by taking advantage of its nesting structure. A particular quantity yielded naturally during the algorithm is shown to be a useful order test statistic, and a more robust order statistic is developed by using the parameter estimate given during the algorithm. By Monte Carlo simulations, the test procedures based on these statistics are confirmed to be valid in spite of the simple construction of the. IPM matrix even in the case where the noise is serially correlated and/or the level is high.