Symmetrical NMR spectroscopy constitutes a vital branch of multidimensional NMR spectroscopy, providing a powerful tool for the structural elucidation of biological macromolecules. Non-Uniform Sampling (NUS) serves as an effective strategy for averting the prohibitive acquisition time of multidimensional NMR spectroscopy by only sampling a few points according to NUS sampling schedules and reconstructing missing points via algorithms. However, current sampling schedules are unable to maintain the accurate recovery of cross peaks that are weak but important. In this work, we propose a novel sampling schedule termed as SCPG (Symmetrical Copy Poisson Gap) and employ CS (Compressed Sensing) methods for reconstruction. We theoretically prove that the symmetrical constraint, apart from sparsity, is implicitly implemented when SCPG is combined with CS methods. The simulated and experimental data substantiate the advantage of SCPG over state-of-the-art 2D Woven PG in the NUS reconstruction of symmetrical NMR spectroscopy.