This technical note aims to design a decentralized control strategy for multiple double-integrator agents to achieve flocking while maintaining an angle-constrained triangulated formation shape in the plane. We design a novel decentralized formation controller that can steer agents to achieve common velocity while meeting some angle constraints; preserve formation rigidity during agents' motion; and be implemented in the absence of the global coordinate system. Due to the rigidity preservation property, the proposed controller guarantees almost global convergence to a formation satisfying predefined angle constraints. Moreover, we give a definition of "sign" for strongly nondegenerate triangulated frameworks. By implementing the proposed control strategy, the target formation shape is guaranteed to be stable provided its sign is identical to that of the initial formation. A simulation example is presented for illustrating effectiveness of the proposed formation controller.