It has been known at least since Chang (1996) that a full Markov model is not identi- fiable for a rooted topology with two terminal taxa without additional assumptions. We shall now prove, under mild conditions, that a non-stationary, strand-symmetric model is identifiable for this topology. This result will provide the foundation for showing that rooted topologies of any size are recoverable, and that the full model is identifiable using joint distributions of states between pairs of taxa. Definition 3.1. We call a matrix M strand-symmetric if it takes the form 3 Identifiability of the Full Model 3.1 Identifiability with a Rooted Two-Taxon Topology Note that if a transition probability matrix is strand-symmetric in this sense, it only fits the usual definition of strand symmetry if the states are properly ordered. Several such orderings are possible. One is ( A, C, G, T ). Definition 3.2. We say that a probability 4-vector π is compositionally asymmetric if it has non-zero elements and π (1) = π (4), π (2) = π (3), π (1) /π (4) = π (2) /π (3), and π (1) /π (4) = π (3) /π (2). We note that any stationary marginal distribution of a strand-symmetric process violates all four of the conditions of compositional asymmetry, provided that the states are again appropriately ordered as ( A, C, G, T ) or similar. However, some distributions that are not the stationary distribution of a strand-symmetric process are included in the set of compositionally asymmetric distributions. The reason for this will become apparent in the following proof. 8 M =    $^{δ}$ α β γ ζ φ η θ θ η φ ζ γ β α δ     .