A non-overlapping and non-conformal domain decomposition method (DDM) is presented for modelling large finite antenna arrays. There are two major ingredients in the proposed DDM: (a) A new second-order transmission condition is introduced, which improves convergence of the iterative process. In contrast to previous high order interface conditions, the new condition uses two second-order transverse derivatives to address the slow convergence issue of both TE and TM evanescent modes. Numerical experiments demonstrate that the convergence of the proposed algorithm is quite insensitive to the size of array. (b) The proposed non-conformal DDM not only permits the use of completely independent discretization for each of the sub-domains, but also allows adjacent sub-domains to be geometrically non-conformal. The benefits of the non-conformal nature of the proposed DDM will be fully enjoyed by a largescale problem of practical interest, which is a 50 by 50 ultra wide band (UWB) array in the presence of a slot frequency selective surface (FSS). Numerical results verify the effectiveness of the proposed method.