We introduce a simple geometrical two-dimensional continued fraction algorithm inspired from dynamical renormalization. We prove that the algorithm is weakly convergent, and that the associated transformation admits an ergodic absolutely continuous invariant probability measure. Following Kosygin and Baldwin, its Lyapunov exponents are related to the approximation exponents which measure the diophantine quality of the continued fraction. The Lyapunov exponents for our algorithm, and related ones also introduced in this article, are studied numerically.