We investigate the global linear stability properties of the quasi-parallel flow in the neighbourhood of the trailing edge of a thin aerofoil, using a WKBJ/multiple scales formulation in the limit of large Reynolds number, as originally developed by Monkewitz, Huerre & Chomaz. We show that the wake is globally linearly unstable to second order in the asymptotic expansion parameter at all Reynolds numbers provided the effective adverse pressure gradient at the trailing edge, which is related to the aerofoil thickness distribution, is sufficiently large. For smaller adverse pressure gradients, there exists a critical Reynolds number above which the flow is globally linearly unstable, but below which it is globally stable. An asymptotic analysis for large wavenumber indicates that the double Blasius profile, corresponding to a zero adverse pressure gradient, may be absolutely unstable.