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A scheme of teleporting a superposition of coherent states |α> and |-α> using a 4-partite state, a beam splitter and two phase shifters was proposed by N. Ba An (Phys. Rev. A, 68, 022321, 2003). The author concluded that the probability for successful teleportation is only 1/4 in the limit |α|→∞ and 1/2 in the limit |α|→∞. In this paper it is shown that the author’s scheme can be altered slightly so as to obtain an almost perfect teleportation for an appreciable value of |α|2. We find the minimum assured fidelity i.e., the minimum fidelity for an arbitrarily chosen information state, which we write MAF in this paper, for different cases. We also discuss the effect of decoherence on teleportation fidelity. We find that if no photons are counted in both final outputs, MAF, is still nonzero except when there is no decoherence and the initial state (the state to be teleported) is even coherent state. For non-zero photon counts, MAF decreases with increase in |α|2 for low noise. For high noise, however, it increases, attains a maximum value and then decreases with |α|2. The average fidelity depends appreciably on the initial state for low values of |α|2 only.