<p>In Narang et al. (Appl Math Comput 275:394–403, 2016), a two-parameter family of Chebyshev-Halley-like iterative schemes for solving nonlinear systems is studied. However, the convergence analyses in their studies are based on Taylor series expansion, which requires the existence of derivatives of the involved operator up to five and seven for iterative schemes of order four and six, respectively. In this paper, we obtain these convergence orders for the respective iterative schemes with assumptions on the derivatives of orders only up to three. We avoid the Taylor series approach to remove the higher-order derivatives of the involved operator. We also provide the semi-local convergence analysis (which is not given in Narang et al. (Appl Math Comput 275:394–403, 2016)) in a more general Banach space. Moreover, unlike the existing studies, our semi-local and local convergence analyses are based on the same set of assumptions, where the authors generally use one set of assumptions for semi-local convergence analysis and another for local convergence analysis. Numerical examples are also discussed to illustrate our theoretical findings. Also, we have shown the symmetrical dynamics of the considered schemes via examples.</p>