We consider the bifurcating solutions for the Ginzburg–Landau equations when the superconductor is a film of thickness 2d submitted to an external magnetic field. We refine some results obtained earlier [1] on the stability of bifurcating solutions starting from normal solutions. We prove, in particular, the existence of curves d [map ] κ0(d), defined for large d and tending to 2−1/2 when d [map ] +∞ and κ [map ] d1(κ), defined for small κ and tending to √5/2 when κ [map ] 0, which separate the sets of pairs (κ, d) corresponding to different behaviour of the symmetric bifurcating solutions. In this way, we give in particular a complete answer to the question of stability of symmetric bifurcating solutions in the asymptotics ‘κ fixed-d large’ or ‘d fixed-κ small’.