This paper addresses the problem of the non unitary joint diagonalization of a given set of complex matrices. We focus on gradient based algorithms. A new algorithm based on a relative gradient approach is suggested. Its algorithmic complexity is established and the optimal stepsize is calculated algebraically at each iteration to decrease the number of iterations required to reach the convergence while discarding the often difficult stepsize choice problem. Computer simulations are provided to illustrate the behavior of this algorithm in different contexts. It is also compared with other existing joint diagonalization algorithms.