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We present a new set of triangular patch basis functions. It retains the same properties as the traditional RWG basis, but is capable of representing any linear current distribution over each triangle. With this improvement, the proposed basis is much less sensitive to the meshing scheme. Moreover, it provides a better representation of the actual current distribution, leading to a faster convergence of the moment method solution. All of this can be achieved with about the same computational complexity of the RWG basis.