The terminal control problem for linear systems having phase trajectory controlled jumps is considered. The controls are piecewise constant functions. Direct and dual exact algorithms are suggested based on a general approach developed earlier for linear programming problems by R. Gabasov and F. M. Kirillova [”Linear programming methods. Part 3. Special problems” (1980; Zbl 0484.90067)]. The algorithms consist of 3 procedures: control change, support change and sorting, the latter of them ensures finiteness of the algorithm.