In the group communication which has multiple data streams and various access privileges, it is necessary to provide group access control. The group members having the same access privilege are classified into one class, and the classes form a hierarchy based on the access relations. Then each class is assigned to a secret key. In the previous schemes, a single logical key graph is constructed from the hierarchy and each member always holds all secret keys of the classes he can access in the proactive manner. Thus, higher-privileged members hold more keys then lower-privileged members. However, if the hierarchy is large, each member manages too many keys and the size of multicast message in rekeying increases in proportion to the size of the hierarchy. Moreover, most of the members access a small portion of multiple data streams simultaneously. Therefore, it is redundant to receive rekeying message and update the keys in which he is not currently interested. In this paper, we present a new key management scheme that takes a reactive approach in which each member obtains the key of a data stream only when he wants to access the stream. Each member holds and updates only the key of the class he belongs. If he wants to get the key of other class, he derives it from his key and the public parameter. Proposed scheme considerable reduces the costs for rekeying, especially in the group where access relations are very complex and the hierarchy is large. Moreover, the scheme has another advantage that it easily reflects the change of access relations.