The Glimm's scheme is known to give accurate approximate solutions for many complex problems on one-dimensional domains. Although it has been recently applied using an ADI method for multidimensional domains with structured meshes, it is known that this scheme can not be applied for unstructured meshes. Following Glimm's idea, a new scheme has recently been introduced in order to cope with the very specific problem of front propagation in multidimensional domains and for unstructured meshes. The latter relies on a fractional step approach in which the sharpening step involves a random choice. Finally, the scheme is very simple to implement, even in a multi-processor framework, and it appears to give satisfactory results in terms of accuracy and convergence rate. The talk will be dedicated to this new scheme. It will be presented in details and its behavior will be illustrated by some numerical experiments. Thanks to its simplicity, some theoretical results can be exhibited, in particular a proof of convergence of the scheme.