We consider a discrete-time orthogonal spline collocation scheme for solving Schrödinger equation with wave operator. The scheme is proposed recently by Wang et al. (J Comput Appl Math 235 (2011), 1993-2005) and is showed to have high-order convergence rate when a parameter θ in the scheme is not less than \documentclass{article} \usepackage{amsmath,amsfonts, amssymb}\pagestyle{empty}\begin{document}$\frac{1}{4}$\end{document}. In this article, we show that the result can be extended to include \documentclass{article} \usepackage{amsmath,amsfonts, amssymb}\pagestyle{empty}\begin{document}$\theta\in(0,\frac{1}{4})$\end{document} under an assumption. Numerical example is given to justify the theoretical result. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013 [ABSTRACT FROM AUTHOR]