The cubic Laves phase of YCo2 is near a transition from a paramagnetic to a magnetically ordered state. Self-consistent energy-band calculations yield the total energy and the magnetic moment as functions of volume. The new fixed spin-moment (FSM) method, which allows one to calculate the total energy as an explicit function of the magnetisation, is introduced. At the theoretical equilibrium volume YCo2 is found to be a strongly enhanced Pauli paramagnet, but at a slightly larger lattice constant a metamagnetic transition seems possible. Its occurrence can be understood on the basis of a double minimum in the total energy obtained from the present FSM calculations, which lead to an estimated critical field of about 350 T. In the magnetic state the Y moment is coupled antiferromagnetically to the Co moment.