In this work, we give a new stability criterion for planar periodic Hamiltonian systems, improving the results from the literature. The method is based on an application of the Floquet theory recently established in [J.J. DaCunha, J.M. Davis, A unified Floquet theory for discrete, continuous, and hybrid periodic linear systems, J. Differential Equations 251 (2011) 2987-3027], and the use of a new definition for a generalized zero. The results obtained not only unify the related continuous and discrete ones but also provide sharper stability criteria for the discrete case. (C) 2012 Elsevier Ltd. All rights reserved.