A　graph　of　order　n　is　p-factor-critical,　where　p　is　an　integer　of　the　same　parity　as　n,　if　the　removal　of　any　set　of　p　vertices　results　in　a　graph　with　a　perfect　matching.　1-factor-critical　graphs　and　2-factor-critical　graphs　are　well-known　factor-critical　graphs　and　bicritical　graphs,　respectively.　It　is　known　that　if　a　connected　vertex-transitive　graph　has　odd　order,　then　it　is　factor-critical,　otherwise　it　is　elementary　bipartite　or　bicritical.　In　this　paper,　we　show　that　a　connected　vertex-transitive　non-bipartite　graph　of　even　order　at　least　6　is　4-factor-critical　if　and　only　if　its　degree　is　at　least　5.　This　result　implies　that　each　connected　non-bipartite　Cayley　graph　of　even　order　and　degree　at　least　5　is　2-extendable.　©　2016,　Australian　National　University.　All　rights　reserved.