  This year, a second generation of coronagraphs dedicated to high-contrast
direct imaging of exoplanets is starting operations. Among them, SPHERE,
installed at the focus of the UT3 Very Large Telescope, reaches unprecedented
contrast ratios up to $10^{-6}$ -$ 10^{-7}$, using eXtreme Adaptive Optics and
the Angular Differential Imaging (ADI) techniques.
  In this paper, we present a new method called Keplerian-Stacker that improves
the detection limit of high contrast instruments like SPHERE, by up to a factor
of 10. It consists of observing a star on a long enough period to let a
hypothetical planet around that star move along its orbit. Even if in each
individual observation taken during one night, we do not detect anything, we
show that it is possible, using an optimization algorithm, to re-center the
images according to keplerian motions (ex: 10-100 images taken over a long
period of typically 1-10 years) and detect planets otherwise unreachable. This
method can be used in combination with the ADI technics (or possibly any other
high contrast data reduction method) to improve the Signal to Noise Ratio in
each individual image, and to further improve the global detection limit. It
also directly provides orbital parameters of the detected planets, as a
by-product of the optimization algorithm.
