Pressure effects on the stability of magnetic phases in La(1.4)Sr(1.6)Mn(2)O(7) have been studied using magnetization measurements and neutron diffraction. At ambient conditions this material is a quasi-two-dimensional ferromagnet. On cooling it becomes ordered three dimensionally: at 90 K La(1.4)Sr(1.6)Mn(2)O(7) it becomes an antiferromagnet, and at 65 K it undergoes a transition into a ferromagnetic phase. Using neutron diffraction techniques on a single crystal of La(1.4)Sr(1.6)Mn(2)O(7) it has been shown that these two magnetic phases belong to a single structural phase and do not coexist at low temperatures. The application of pressure enhances the antiferromagnetic correlations between the Mn(2)O(9) bilayers.