Previous work by Hauge and Martin-Löf discussing the generalized Langevin equation for Brownian motion as a contraction from the more fundamental but still phenomenological description of a particle immersed in an incompressible fluid governed by fluctuating hydrodynamics with stick boundary condition is extended to the case of a Brownian particle with arbitrary shape and withslip boundary condition. The motivation for this extension is the fact that the latter condition naturally arises in a treatment of the problem from first principles.