In the context of static analysis based on Abstract Interpretation, we propose a new abstract operator modeling the \emph{split} of control flow paths: the goal of the operator is to enable a more efficient analysis when using abstract domains that are computationally expensive, having no effect on precision. Focusing on the case of conditional branches guarded by numeric linear constraints, we provide a preliminary experimental evaluation showing that, by using the split operator, we can achieve significant efficiency improvements for a static analysis based on the domain of convex polyhedra. We also briefly discuss the applicability of this new operator to different, possibly non-numeric abstract domains.