Abstract In practical engineering, many control problems usually can be transformed into solutions of the discrete algebraic Riccati equation (DARE), which has two matrix inverse operations formally. In this paper, first, by the relationship between properties of the matrix Schur complement and partitioned representation of inverse matrix, we change the DARE with twice inversions into an equivalent form with once inversion and propose a corresponding iterative algorithm. Next, for a special case of DARE, we deformed this DARE into a new equivalent one. For the equivalent form, we propose a new iterative algorithm in an inversion-free way. Furthermore, for these algorithms, we prove their monotone convergence and give the analysis of their errors. Last, comparing with some existing work on this topic, corresponding numerical examples are given to illustrate the superiority and effectiveness of our results.