Designing a group key management scheme for group communication in wireless sensor network is a challenging task given the limited energy, computational power and memory of the sensor nodes. A group key management scheme should satisfy backward secrecy and forward secrecy security requirements in case of sensor revocation and new sensor join respectively. All the existing schemes are analyzed for their security under passive attack model. However, active outsider adversary model in which as adversary is allowed to compromise the legitimate sensor of the group is a strong model. In this work, we show that the key management schemes for wireless sensor networks based on bivariate polynomials, exclusive basis systems, key tree etc are not secure against active outsider model. In particular, we show that an outside adversary by compromising the legitimate sensor could obtain access not only to the current session group key but also the past group keys. Adversary can get the past keys despite the fact that the sensor nodes have erased the past group keys. To secure them against active adversary all the keys should be updated for every rekeying event which incurs additional cost of computation and communication for managing keys. We also give the methods to secure the schemes under active outsider adversary model.