  In this talk we report on our study of two-colour lattice QCD with N_f=4
staggered fermion degrees of freedom with equal electric charge q in a
homogeneous magnetic field B at non-zero temperature T. We find indications for
a non-monotonic behaviour of the critical temperature as a function of the
magnetic field strength and, as a consequence, for the occurence of `inverse
magnetic catalysis' within the transition region for magnetic fields in the
range 0 < qB < 0.7 GeV^2.
