Abstract: In this paper new matrices of the Cayley-Klein parameters are used to represent composition of several consecutive finite rotations of rigid body. The general commutative rules of multiplication for these matrices is obtained. Furthermore, by using these matrices it is convenient to prove the theorem on finite rotation of rigid body. The result obtained in this paper is concise and easy to remember, and can be used to calculate vehicle attitude.

Key words: Cayley-Kiein parameters, rigid body, finite rotation, vehicle attitude