Night-migratory songbirds are remarkably proficient navigators1. Flying alone and often over great distances, they use various directional cues including, crucially, a light-dependent magnetic compass2,3. The mechanism of this compass has been suggested to rely on the quantum spin dynamics of photoinduced radical pairs in cryptochrome flavoproteins located in the retinas of the birds4-7. Here we show that the photochemistry of cryptochrome 4 (CRY4) from the night-migratory European robin (Erithacus rubecula) is magnetically sensitive in vitro, and more so than CRY4 from two non-migratory bird species, chicken (Gallus gallus) and pigeon (Columba livia). Site-specific mutations of ErCRY4 reveal the roles of four successive flavin-tryptophan radical pairs in generating magnetic field effects and in stabilizing potential signalling states in a way that could enable sensing and signalling functions to be independently optimized in night-migratory birds.