<p>The symmetric alternating direction method of multipliers (ADMM) is an effective algorithm for solving separable optimization problems with linear constraints. In the convex setting, its theoretical foundations have been well established. Recently, with the emergence of numerous nonconvex optimization problems in fields such as machine learning and image processing, the convergence properties of symmetric ADMM in the nonconvex settings have attracted significant attention. However, existing research still has certain limitations, including the requirement that one matrix in the linear constraints must be an identity matrix or a scalar matrix, the restriction of identical step sizes for two dual variable updates, or discrepancies between theoretical assumptions on problem data and practical applications. To address these issues, this paper conducts a further study on symmetric ADMM and establishes its convergence properties in the full nonconvex setting. Finally, preliminary numerical experiments on regression problems and CT image denoising demonstrate the efficiency of the symmetric ADMM.</p>