The concept of subgame perfect equilibrium is broadly accepted in the theory of non-cooperative games in extensive form and offers a method of equilibrium calculation called backward induction. Nevertheless, there often exist many other equilibria, which might also be interesting, because they require some coordination by groups of players. The most frequently cited literature does not provide an effective mechanism to identify all equilibria of games in extensive form. The present paper gives an answer to this problem. First, a general characterization of equilibrium is derived. This result offers a way to specify an algorithm, which lists all paths to terminal points of the game arising from equilibrium strategies. Finally, an application of the results to the decision problem of the Cuban Missile Crisis will be discussed.