This paper investigates multiuser interference (MUI) cancellation for millimeter-wave (mmWave) beamforming in communication systems. We propose a linear algorithm, termed iterative dual orthogonal projections (DOP), which alternates between two orthogonal projections: one to eliminate MUI and the other to refine combiners, ensuring empirical convergence in spectral efficiency. Simulation results show that, with each iteration, the spectral efficiency of each user converges rapidly, closely approaching the theoretical optimum determined by dirty paper coding (DPC), surpassing existing linear benchmarks while maintaining low computational complexity. Furthermore, the proposed DOP algorithm is extended to support both fully-digital and hybrid beamforming architectures.