The modulo 2^n ± 1 are the most applied modulo set in residue number system (RNS). The modulo adder 2^n-1 is very important due to its variety of applications in DSP, like addition/subtraction and multiplication in digital filters, cryptography, fault detection, fault correction and checksum. In this article, by applying carbon nanotube transistors based on End Around Carry structure, a modulo adder 2^n-1 is implemented. The problems are analyzed and in order to fix them and improve the orbital parameters, a new design is proposed. Through this design, the problem for two representations of zero are solved, and by taking advantage of a structure for fast calculation of carry, the orbital parameters are upgraded. The circuits are simulated by Hspice simulation tools and their performances are verified. Simulation results confirm the superior performance of this proposed design compared to the EAC (End Around Carry) structure.