We consider the convergence behavior using the relaxed Peaceman–Rachford splitting method to solve the monotone inclusion problem 0 in (A + B)(u), where A, B: Re ^n rightrightarrows Re ^n are maximal beta -strongly monotone operators, n ge 1 and beta > 0. Under a technical assumption, convergence of iterates using the method on the problem is proved when either A or B is single-valued, and the fixed relaxation parameter theta lies in the interval (2 + beta , 2 + beta + min { beta , 1/beta }). With this convergence result, we address an open problem that is not settled in Monteiro et al. (Computat Optim Appl 70:763–790, 2018) on the convergence of these iterates for theta in (2 + beta , 2 + beta + min { beta , 1/beta }). Pointwise convergence rate results and R-linear convergence rate results when theta lies in the interval [2 + beta , 2 + beta + min {beta , 1/beta }) are also provided in the paper. Our analysis to achieve these results is atypical and hence novel. Numerical experiments on the weighted Lasso minimization problem are conducted to test the validity of the assumption.