Abstract: This paper addresses the waveform adaptation issue of multiple competitive Multiple-In Multiple-Out Cognitive Radios (MIMO-CR) respectively maximizing their information rates under the interference-temperature constraint of primary users. This issue is formulated as a Nash equilibrium issue from a non-cooperative game theoretic viewpoint, conditions for the existence and uniqueness of the Nash equilibrium are provided and a decentralized Iterative Water-Filling Algorithm (IWFA) with a punishing price is proposed to solve the above Nash equilibrium issue, the punishing price is imposed on the interference generated by MIMO-CRs in order to make the interference-temperature constraint satisfied while MIMO-CRs achieve the Nash equilibrium. Simulation results show, when compared to the classical IWFA which does not consider the interference-temperature constraint, the proposed algorithm satisfies the interference-temperature constraint and hence is applicable to cognitive radio networks.