Many real-world graphs are directed, but standard graph neural networks are often designed for undirected edges, and simple directed adaptations can worsen oversmoothing and gradient instability. This work introduces Dune, a directed unitary graph neural network with edge features that extends unitary graph convolutions while retaining their stability guarantees. The unitary operator can also be used in hybrid graph-transformer architectures as a source of positional information. The method avoids exponential oversmoothing, remains trainable at large depths, and improves performance across directed-graph benchmarks.