Recently, Liu et al. [Q. B. Liu, G. L. Chen, J.Huang, On the parallel GSAOR method for block diagonallydominant matrices, Appl. Math. Comput . 215 (2009), 707–715] study the convergence of the parallel multisplitting generalized SAOR iterative methods based on the generalized AOR iterative method for solving a linear system whose coefficient matrix is a block diagonally dominant matrix or a generalized block diagonal dominant matrix. In this paper, we extend the domain of convergence from 1≤ω i < 2/(1+ μ 1 ( PMQ )) and 1≤ω i < 2/(1+ μ 2 ( PMQ )) to 0 < ω i < 2/(1 + μ 1 ( PMQ )) and 0 < ω i < 2/(1 + μ 2 ( PMQ )) for the parallel multisplitting generalized SAOR iterative methods.