In an analogy from symmetric ordinary differential equation numerical integrators, we derive a three-stage, weak 2nd-order procedure for Monte-Carlo simulations of Itô stochastic differential equations. Our composite procedure splits each time step into three parts: an h/2 h / 2 -stage of trapezoidal rule, an h h -stage martingale, followed by another h/2 h / 2 -stage of trapezoidal rule. In n n time steps, an h/2 h / 2 -stage deterministic step follows another n−1 n - 1 times. Each of these adjacent pairs may be combined into a single h h -stage, effectively producing a two-stage method with partial overlap between successive time steps
