Cognitive radio (CR) is an intelligent radio system and is able to share the spectrum with licensed users (LU). By adopting adaptive beam forming techniques, CR can reuse the spectrum with LU via directing main beams towards CR users while displaying nulls towards LU. In this article, we present a new distributed beam forming (DB) technique, and study the performance of its application to decentralized CR networks. The presented DB method only controls the phase of the transmitted signal of each CR node in the CR network, and therefore, it is called phase-only DB (PODB) method. It can be implemented at each node independently with only prior knowledge of its own location, and directions of distant CR (DCR) users and LU. The average beam pattern and the average gains for an arbitrary number of CR nodes of PODB method are discussed, showing that CR nodes can constructively transmit signals to DCR users with less interferences to LU via employing the PODB method to form and direct main beams towards directions of DCR users while nulls towards directions of LU. PODB proves to be a green DB method by prolonging the lifetime of the CR network due to effective battery power consumptions at CR nodes. The cumulative distributed function of the beam pattern for a large number of CR nodes is derived and analysed to demonstrate that the PODB method increases the possibility that the transmitted power of the whole CR network at the directions of LU is lower than a certain threshold, which guarantees that CR network causes less disturbing effect to LU.Keywords: distributed beam forming, collaborative beam forming, cognitive radio networks, phase-only distributed beam forming, null-steering distributed beam forming, green cognitive radio networks