Abstract: The result about controllability canonical form for multi-input nonlinear control systems by the algebraic method established is refined in this paper. This problem was studied in many papers mainly by differential geometric method which is not easy to possess and apply for engineers. Two complete sets of sufficient conditions for existence of state transformation which converts the nonlinear control system to the controllability canonical form are given . Then ,a procedure for the calculation of the controllability indices is established. After this, a special case which is called uniform controllability canonical form is considered. Furthermore, the uniqueness of the canonical form in the framework of a given procedure for constructing the state transformation is discussed.

Key words: multi-input nonlinear control systems, controllability canonical form, state trans-formation