The ηT pairing on supersingular is one of the most efficient algorithms for computing the bilinear pairing . The rfr pairing defined over finite field F3n has embedding degree 6, so that it is particularly efficient for higher security with large extension degree n. Note that the explicit algorithm over F3n in  is designed just for n Ξ 1 (mod 12), and it is relatively complicated to construct an explicit algorithm for n ≢ 1 (mod 12). It is better that we can select many n's to implement the r¡T pairing, since n corresponds to security level of the ηT pairing. In this paper we construct an explicit algorithm for computing the ηT pairing with arbitrary extension degree n. However, the algorithm should contain many branch conditions depending on n and the curve parameters, that is undesirable for implementers of the ηT pairing. This paper then proposes the universal ηT pairing (ηT pairing), which satisfies the bilinearity of pairing (compatible with Tate pairing) without any branches in the program, and is as efficient as the original one. Therefore the proposed universal ηT pairing is suitable for the implementation of various extension degrees n with higher security.