The fidelity of the generated Schr(o)dinger Cat state (SCS) of a single trapped ion in the Lamb-Dicke approximation is discussed. The results show that the fidelity significantly decreases with the values of Lamb-Dicke parameter η and coherent state amplitude α increasing. For η = 0.20 and α = 3, the typical values of experimental parameters, the fidelity is rather low (30%). A scheme for generating the SCS is proposed without making the Lamb-Dike approximation in laser-ion interaction, and the fidelity of the generated SCS is about 99% for the typical values of experimental Lamb-Dicke parameters.