In this paper, the new alternative method for the determination of the set of all minimal realisations of the positive two-dimensional hybrid linear systems in a second Fornasini-Marchesini (IIF-M) model based on the two-dimensional digraphs theory has been presented. In addition, all realisations in the set are minimal. For the proposed method, parallel computing algorithm was constructed. Algorithm is based on GPGPU (General-Purpose Computing on Graphics Processing Units) computing method to gain needed speed and computational power for a such solution. Proposed method is discussed and illustrated with numerical examples.