The present work represents the first attempt to utilize the idea of recursively generated intermediates (RGI) in the framework of the state-selective multi-reference coupled-cluster method truncated at triple excitations [SS CCSD(T)]. The expressions for stepwise generation of intermediates are so structured that the spin and point symmetry simplifications can be easily applied during computation. Suitable modifications in SS CCSD(T) equations are introduced to allow for optional quasilinearization of nonlinear terms in difficult convergence situations. The computational code is, as expected, much faster than the SS CCSD(T) code without RGI adaptation. This has been numerically demonstrated by potential energy surface (PES) calculation of the HF molecule using a double zeta basis.