Most resource allocation algorithms are based on interference power constraint in cognitive radio networks.Instead of using conventional primary user interference constraint,we give a new criterion called allowable signal to interference plus noise ratio(SINR) loss constraint in cognitive transmission to protect primary users.Considering power allocation problem for cognitive users over flat fading channels,in order to maximize throughput of cognitive users subject to the allowable SINR loss constraint and maximum transmit power for each cognitive user,we propose a new power allocation algorithm.The comparison of computer simulation between our proposed algorithm and the algorithm based on interference power constraint is provided to show that it gets more throughput and provides stability to cognitive radio networks. Most resource allocation algorithms are based on interference power constraint in cognitive radio networks. Instead of using conventional primary user interference constraint, we give a new criterion called allowable signal to interference plus noise ratio (SINR) loss constraint in cognitive transmission to protect primary users. Considering power allocation problem for cognitive users over flat fading channels, in order to maximize throughput of cognitive users subject to the allowable SINR loss constraint and maximum transmit power for each cognitive user, we propose a new power allocation algorithm. The comparison of computer simulation between our proposed algorithm and the algorithm based on interference power constraint is provided to show that it gets more throughput and able to cognitive to radio networks.