The paper presents a technique for the control of quantum mechanical systems based on decompositions of Lie groups. For two level quantum systems a decomposition due to F. Lowenthal is used. This decomposition is a generalization of the classical Euler decomposition for SU(2). The resulting control algorithm allows to steer the state of the system to any desired final configuration. Moreover this algorithm also allows a control arbitrarily bounded in magnitude. For the four level quantum system of two interacting spin 1/2 particles an algorithm is also presented which uses a modification of Cartan decomposition of the Lie group SU(4) and allows to drive of the state to any desired final configuration.