Abstract: Without other addional hypothesis a new formula for all Q-processes is given when the exit boundary of density matrix Q consists of finite points (a non-conservative state corresponding to an exit boundary point ), (theorem 1 ) . This formula is simple and the independent parameters in it have clear probability meaning. It is convenient to get all the solutions of Kalmogorov's forward and backward equations ( theorem 2,3,4). Especially, the formula obtained by the author improves Williams' result when Q is conservative. In the meantime an error in "On the construction problem for Markov chains" is corrected. Because of this error,the formula in the paper does not show all Q-proeesses.