In this paper we examine a two-person zero-sum timing game with the following structure: Each of players I and II has a gun with two bullets and they fight a duel. Both guns are silent so that neither player can determine whether his opponent has fired the bullets or not. Player I is at the place 0 when the duel begins and he can move as he likes and player II is always at the place 1. Accuracy functions, which denote the probability of hitting the opponent when each player fires his bullet, are identical for both players. If player I hits player II without being hit himself first, then the payoff is +1; if player I is hit by player II without hitting player II first, the payoff is -1; if they hit each other at the same moment or both survive, the payoff is 0. The objective of this paper is to obtain the game value and the optimal strategies for the timing game.