We study the structure of the escape orbits for a certain class of interval maps. This structure is encoded in the escape transition matrix b Af of an interval map f, extending the traditional matrix Af which considers the transition among the Markov subintervals. We show that the escape transition matrix is a topological conjugacy invariant. We then characterize the 0–1 matrices that can be fabricated as escape transition matrices of Markov interval maps f with escape sets. This shows the richness of this class of interval maps.