An infinitely diverging channel with a line source of fluid at its vertex is a natural idealization of flow in a finite channel expansion. Motivated by numerical results obtained in an associated geometry (Tutty 1996), we show in this theoretical model that for certain channel semi-angles $\alpha$ and Reynolds numbers $\hbox{\it Re}\,{:=}\,Q/2\nu$ ($Q$ is the volume flux per unit length and $\nu$ the kinematic viscosity) a steady, spatially periodic, two-dimensional wave exists which appears spatially stable and hence plausibly realizable in the physical system. This spatial wave (or limit cycle) is born out of a heteroclinic bifurcation across the subcritical pitchfork arms which originate out of the well known Jeffery-Hamel bifurcation point at $\alpha\,{=}\,\alpha_2(\hbox{\it Re})$. These waves have been found over the range $5\,{\leq}\,\hbox{\it Re}\,{\leq}\,5000$ and, significantly, exist for semi-angles $\alpha$ beyond the point $\alpha_2$ where Jeffery-Hamel theory has been shown to be mute. However, the limit of $\alpha\,{\rightarrow}\, 0$ at finite $Re$ is not reached and so these waves have no relevance to plane Poiseuille flow.