In this paper, we propose DeMuon, a method for decentralized matrix optimization over a given communication topology. DeMuon incorporates matrix orthogonalization via Newton–Schulz iterations—a technique inherited from its centralized predecessor, Muon—and employs gradient tracking to mitigate heterogeneity among local functions. Under heavy-tailed noise conditions and additional mild assumptions, we establish the iteration complexity of DeMuon for finding an approximate stochastic stationary solution. This complexity result matches the best-known complexity bounds of centralized algorithms in terms of dependence on the target tolerance. To the best of our knowledge, DeMuon is the first direct extension of Muon to decentralized optimization with provable complexity guarantees. We conduct preliminary numerical experiments on decentralized transformer pretraining over communication graphs with varying degrees of connectivity, including complete graphs, directed exponential graphs, and ring graphs. Our numerical results demonstrate a clear margin of improvement of DeMuon over widely used decentralized algorithms across different network topologies.