The magnetic properties of BaCoO3 are strongly influenced by the frustration induced by the hexagonal structure. Previously, collinear configurations with ferromagnetically (FM) ordered hexagonal planes stacked antiferromagnetically (AF) along the c-axis (that of the Co chains) were found to be nearly degenerate and an orbitally ordered state (along c) was encountered. Here, we present a study of possible non-collinear magnetic structures in the system. We have used the WIEN2k software, which uses a full-potential, all-electron APW+lo (augmented plane waves plus local orbitals) method in a version adapted for studying non-collinear magnetic configurations. We explore this possibility of a non-collinear arrangement of the magnetic moments within the hexagonal plane, which could lead to a vanishing net magnetization within the plane. Due to the triangular arrangement of the Co chains and resulting frustrations, a simple AF order is not possible with any collinear configuration. Our calculations show that the most stable ordering is FM within the plane.