In this paper, we develop a new approach for the iterative refinement algorithm along with fully mathematical justificationS, which sharpens matrix solution upper bounds for the well-known continuous coupled algebraic Riccati equation (CCARE). Our methodology is studied within a broader framework recently proposed in Xu (in press). Several desirable properties of the algorithm are then established, which include the strict monotonicity and convergence of the sequences generated by the algorithm, thus strengthening the existing results in the literature for computing tighter matrix upper solution bounds for the CCARE. In addition, new admissibility conditions within the general framework are proposed, which guarantee tighter matrix upper solution bounds to be computed from the algorithm. (C) 2013 Elsevier Ltd. All rights reserved.