We consider the linear stability of channel flow of a shearthinning viscoelastic fluid, replicating a instability recently discovered in experimental [1] and theoretical work [2]. We have extended the fluid model to allow for an inelastic shearthinning stress component, and find that this additional contribution always has a stabilising influence on the instability. We conclude that, while shearthinning is critical to the instability, the mechanism is primarily elastic. (C) 2017 Elsevier B.V. All rights reserved.