The Owen value is a modification of the Shapley value for games with a coalition structure. In this paper, we propose another modification of the Shapley value for monotone games with a coalition structure. This new value is a double- extension of the Shapley value in the next sense: the amount obtained by an union coincides with the Shapley value of the union in the quotient game, and the players of each union share this amount proportionally to their Shapley values in the game without unions. We give two characterizations of this new value. The axiomatic systems used here can be compared with parallel axiomatizations of the Owen value.