Low power VLSI circuit design is one of the most important issues in present day technology. One of the ways of reducing power in a CMOS circuit is to reduce the number of transitions on the bus and Bus Invert Coding is a widely popular technique for that. In this paper we introduce a new way of coding called the ShiftInv Coding that is superior to the bus invert coding technique. Our simulation results show a considerable reduction on the number of transitions over and above that obtained with bus invert coding. Further, the proposed technique requires only 2 extra bits for the low power coding, regardless of the bit-width of the bus and does not assume anything about the nature of the data.