Consider the second order Hamiltonian system
where is a symmetric matrix valued function, and denotes the gradient of with respect to . As usual, a solution of this problem is homoclinic to 0 if and as . The well-known Ambrosetti-Rabinowitz (AR) condition states that there exists a constant such that for all and all . In this paper, the existence of homoclinic orbits is obtained without the (AR) condition but using the concentration-compactness principle and the fountain theorem.