To construct Q process for general cases, it is usually assumed that the matrix Q is conservative. Under this assumption, W. Feller [Ann. Math. 65, 527-570 (1957; Zbl 0084.355)] has constructed all Q processes which satisfy Kolmogorov’s forward equation with both the exit and the entrance boundaries being finite. The author has also constructed all the Q processes in the same case. D. Williams [Z. Wahrscheinlichkeitstheor. Verw. Geb. 3, 227-246 (1964; Zbl 0143.198)] (it is assumed that each state of the minimal Q process is noncurrent) and K. L. Chung [Acta Math. 110, 19-77 (1963; Zbl 0292.60121) and ibid. 115, 111-163 (1966; Zbl 0315.60041)] have examined the construction of all Q processes only with finite exit boundary, independently. In this paper, it is not required that the matrix should be conservative. We have constructed all the Q processes when the matrix Q has a finite set of nonconservative states and a finite exit boundary.