A procedure is put forward for the specificationof a suitable phase diagram for a uniaxial system with a higher-order anisotropy which undergoesa spin-reorientation transition via coherent rotation of magnetizationin an applied field of arbitrary strength and direction.The approach generalises recent studies for a field applied in one of the principal directions.The analysis is valid for bulk and thin-film systems and is relevant to all experimental techniques which involve the implementation of an external field. The representation is especially promising in the context of thickness-driven transitions in ultrathin systems. It is generally valid, beyond the uniaxial restriction, for any remagnetization process which takes place within a given plan