There has recently been interest in the use of orthonormal bases for the purposes of SISO system identification. Concurrently, but separately, there has also been vigorous work on estimation of MIMO systems by computationally cheap and reliable schemes. These latter ideas have collectively become known as `4SID' methods. This paper is a contribution overlapping these two schools of thought by showing how general orthonormal bases may be generated to form model structures suitable for identification of MIMO systems using only simple calculations. In contrast to general prediction error methods and in common with 4SID schemes the estimation algorithms involved are computationally simple. However, a distinguishing feature of the orthonormal basis approach described here is that significant prior knowledge about system poles may be included in the estimation problem.