Abstract: This paper is concerned with the global existence of dissipative solutions to the Camassa–Holm equation after wave breaking. By introducing a new set of independent and dependent variables, the evolution problem is rewritten as an O.D.E. in an L^∞ space, containing a non-local source term which is discontinuous but has bounded directional variation along a suitable cone of directions. For a given initial condition, the Cauchy problem has a unique solution obtained as fixed point of a contractive integral transformation. Returning to the original variables, we obtain a semigroup of global dissipative solutions, defined for every initial data in H¹, and continuously depending on the initial data. The new variables resolve all singularities due to possible wave breaking and ensure that energy loss occurs only through wave breaking.