When applied to the simulation of bi-fluid incompressible flow, the level set method does not ensure mass conservation of each fluid. Now this needs to be enforced. In this paper, we propose a complementary local mass conservation based on a weak formulation of the advection of the interface characteristic function. We first apply our method to the advection of a discontinuous concentration. Secondly, we couple our method with incompressible two-phase flow simulation and validate it on test cases where one fluid separates in disconnected parts (motion of two separated liquid volumes, water column falling on an obstacle).