Abstract. I will present a new mechanism to relax the Cosmological Constant (CC), that is, to dynamically reduce the CC from an initially large value to a small final one. The mechanism is present provided boost invariance is 'slightly' broken, and the initial CC is negative. An interesting feature of this mechanism is that the relaxation operates during the standard Big Bang cosmology. I will present the basic idea and discuss the constraints arising from observational bounds and from naturalness.