The detection of change-points in a spatially or time-ordered data sequence is an important problem in many fields such as genetics and finance. We derive the asymptotic distribution of a statistic recently suggested for detecting change-points, thus establishing its validity. Simulation of its estimated limit distribution leads to a new and computationally efficient change-point detection algorithm, which can be used on very long signals. To finish, we briefly assess this new algorithm on one- and multi-dimensional data.