In this paper we consider the class of simple graphs defined by excluding, as induced subgraphs, even holes (i.e. chordless cycles of even length). These graphs are known as even-hole-free graphs. We prove a decomposition theorem for even-hole-free graphs, that uses star cutsets and 2-joins. This is a significant strengthening of the only other previously known decomposition of even-hole-free graphs, by Conforti, Cornuéjols, Kapoor and Vušković, that uses 2-joins and star, double star and triple star cutsets. It is also analogous to the decomposition of Berge (i.e. perfect) graphs with skew cutsets, 2-joins and their complements, by Chudnovsky, Robertson, Seymour and Thomas. The similarity between even-hole-free graphs and Berge graphs is higher than the similarity between even-hole-free graphs and simply odd-hole-free graphs, since excluding a 4-hole, automatically excludes all antiholes of length at least 6. In a graph that does not contain a 4-hole, a skew cutset reduces to a star cutset, and a 2-join in the complement implies a star cutset, so in a way it was expected that even-hole-free graphs can be decomposed with just the star cutsets and 2-joins. A consequence of this decomposition theorem is a recognition algorithm for even-hole-free graphs that is significantly faster than the previously known ones.