Spectrum leasing is one of the cognitive radio models, where a primary user leases its spectrum resources for secondary user in exchange for cooperation. In  cooperative communication with beamforming (BF) in spectrum leasing was proposed for primary secure communications. However, interference is caused to the primary user from secondary user with its scheme. Therefore, we focus on cooperative communications where secondary users use orthogonal BFs that do not affect primary user. We consider the effects of secondary cooperation and the knowledge of eavesdropper's channel state information (CSI) on the cooperative communications. By simulation, we evaluate primary secrecy capacity, primary secrecy capacity outage probability, secondary sum throughput, and primary throughput. We show that secondary transmit BFs in spectrum leasing are effective for both primary and secondary systems in terms of primary secure communications without any interference from secondary user and with small degradation of the secondary throughput.