In this study, a novel constellation algorithm for application in Discrete Multi Tone (DMT) modulation is presented. As the signal space diagram obtained is similar to snail, we have called the resulting modulation scheme as Snail Shift Keying (SSK), whose major property is its non-symmetric configuration where demands of subscribers can be prioritized conveniently. Quadrature Amplitude Modulation (QAM) and SSK, with the same power, have been applied to the DMT system with AWGN channels. Compared to a well-known QAM modulation scheme, based on the simulation results, the constellation algorithm presented has an improved Bit Error Rate (BER) performance with the same complexity in implementation.