Homoclinic orbits for a time-periodic Hamiltonian system
are found, assuming that
is a hyperbolic equilibrium point and that
has global superquadratic growth in
. They are obtained as local
- limits of certain nontrivial
-periodic solutions of
, where the hyperbolicity prevents them from shrinking to zero. This approach extends results by Rabinowitz for second order Hamiltonian systems, and it differs from corresponding results by Coti-Zelati, Ekeland & Séré and Hofer & Wysocki. The references are given in the paper.