The cubic Heusler compound Mn1.5FeV0.5Al with the L21 Heusler structure is the first fully compensated half-metallic ferrimagnet with 24 valence electrons. The ferrimagnetic state can be tuned by changing the composition such that the compensation point appears at finite temperatures ranging from 0 K up to 226 K, while retaining half-metallicity in the system. In this paper, the structural, magnetic and transport properties of the Mn-Fe-V-Al system are discussed. Magnetic reversal and a change of sign of the anomalous Hall effect were observed at the compensation point, which gives rise to a sublattice spin-crossing. These materials present new possibilities for potential spintronic devices because of their advantageous properties such as imperceptibility to external fields, lower power consumption and ultrafast switching in the THz region.