Non-orthogonal multiple access (NOMA) has been widely identified as an effective scheme for boosting transmission rate by sharing the spectrum resources among multiple users. In this paper, a two-user multiple-input multiple-output (MIMO) NOMA network is considered. User 1 requires a confidential message that should be kept secret from user 2. User 2 is another NOMA user in the network who asks for a private message but with no secrecy requirement. The two NOMA users can dynamically access the spectrum resource and each user can make full use of that when the other is idle. A signaling design is proposed to enhance security performance for user 1 and reach a higher transmission rate for user 2 simultaneously. The corresponding nonconvex capacity problem is first reformulated into a weighted sum-rate maximization problem by applying the block successive maximization method and generalizing the zero duality gap. Then, a new signaling method is developed to achieve the secrecy capacity region. For the multiple-input single-output (MISO) NOMA case, we reveal a hidden convexity and transform the nonconvex problem into a semidefinite program. We prove that the optimal input covariance matrices will always have a rank less or equal to one. Therefore, beamforming is the optimal transmit strategy in this case. Numerical results demonstrate the effectiveness of the developed signaling design. Specifically, it largely increases the transmission rate compared with generalized singular value decomposition (GSVD)-based MIMO-NOMA and is thousands of times faster than brute-force search.