In geometric active contour algorithms, a re-initialization step must be performed by the level set function to remain close to a signed distance function, in order to avoid numerical instabilities. We propose a new re-initialization method that may be employed as a standalone method to recover the signed distance condition, or may be embedded directly into a variational framework as an additional term for the energy functional. Its purpose is to make the pixels near the propagating contour be less affected by the re-initialization. Experimental results show that whereas previous approaches change the position of the zero level set, our method keeps it virtually unchanged.