To improve the traditional subspace data fusion （SDF） algorithm with multiple arrays in terms of degree of freedom （DOF） and accuracy， a direct position determination algorithm for non-circular （NC） signals with multiple arrays is proposed by exploiting the NC characteristics and the concept of reduced-dimension （RD）. Specifically， the NC characteristics are used to obtain the extended spatial information， which contributes to the extended array aperture and enhanced DOFs. However， this leads to the expensive high-dimension search. As a result， the concept of RD is introduced to discard the NC phase and then construct the RD spectrum search function based on SDF. Compared with the traditional SDF algorithm， the superiorities of the proposed algorithm in DOF and position performance are corroborated by numerical results. Besides， without losing the estimation performance， it significantly reduces the complexity.