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 1/4. In this article, we show that the result can be extended to include θ ∈ (0,1/4) under an assumption. Numerical example is given to justify the theoretical result. © 2012 Wiley Periodicals, Inc.