In previous works, the Local Linearization method has been expanded for the simulation of a speciÖc type of stochastic di§erential equations driven by semimartingales, namely equa- tions with additive noise. The e§ectiveness of the resulting Local Linear approximation was shown by means of simulations, and a strong convergence result was also obtained for such approximation. In this note, the Local Linearization method is extended to a notably wider class of equations, and the resulting Local Linear approximations are proved to be bounded and convergent uniformly on compacts in probability.