Model order reduction is a research direction which has provided interest to many scientists recently. A large number of order reduction algorithms have been introduced in many different approaches among which retaining the important poles of the original system in the reduced root system is a dominant approach with many advantages.

This paper presents a new model in order reduction algorithm for both stable and unstable systems, based on the idea of keeping the dominant poles of the original system in the order reduction process. This algorithm transforms matrix  of the higher-order original system to upper - triangle matrix on which the poles are arranged basically on - and - mixed dominant index on the main diagonal of the upper – triangle matrix so that error becomes small and the dominant poles are preserved. The illustration shows the correctness of the model order algorithm.