The L1₀ crystal structure underlines an important class of chemically ordered alloys that exhibits uniaxial magnetocrystalline anisotropy. The near-equiatomic L1₀-FeNi extracted from meteorites has demonstrated intriguing magnetic properties for permanent magnet applications. However, the synthesis of this chemically ordered non-cubic structure has been a longstanding challenge. Here, we demonstrate the absence of cubic symmetry in near-equiatomic Fe-Ni nanoparticles synthesized by picosecond-pulsed laser ablation in liquids. The non-cubic phase detected in these particles can only be L1₀-FeNi or hexagonal close-packed (HCP) FeNi, and the absence of cubic symmetry was unequivocal. The orientation relationship between the non-cubic phase and the adjacent cubic phase was characterized by a series of transmission electron microscopy (TEM) techniques, which consistently suggests that the formation of the non-cubic phase involves a martensitic transformation process.