Summary: A quadratic Lyapunov function is demonstrated for the non-invertible planar Ricker map \((x, y) \mapsto (xe^{r-x-\alpha y}, ye^{s-y-\beta x})\) which shows that for \(\alpha\), \(\beta > 0\), and \(0 < r\), \(s \leq 2\) all orbits of the planar Ricker map converge to a fixed point. We establish that for \(0<r\), \(s<2\), whenever a positive equilibrium exists and is locally asymptotically stable, it is globally asymptotically stable (i.e. attracts all of \((0, \infty)^2)\). Our approach bypasses and improves on methods that rely on monotonicity, which require \(0 < r\), \(s \leq 1\). We also use the Lyapunov function to identify the one-dimensional stable and unstable manifolds when the positive fixed point exists and is a hyperbolic saddle.