  In this paper, a higher-order time-discretization scheme is proposed, where
the iterates approximate the solution of the stochastic semilinear wave
equation driven by multiplicative noise with general drift and diffusion. We
employ a variational method for its error analysis and prove an improved
convergence order of 3/2 for the approximates of the solution. The core of the
analysis is Holder continuity in time and moment bounds for the solutions of
the continuous and the discrete problem. Computational experiments are also
presented.
