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In this paper, a higher-order time-discretization scheme is proposed, wherethe iterates approximate the solution of the stochastic semilinear waveequation driven by multiplicative noise with general drift and diffusion. Weemploy a variational method for its error analysis and prove an improvedconvergence order of 3/2 for the approximates of the solution. The core of theanalysis is Holder continuity in time and moment bounds for the solutions ofthe continuous and the discrete problem. Computational experiments are alsopresented.

Higher order time discretization for the stochastic semilinear wave equation with multiplicative noise