In most communication systems, power and bandwidth are limited. To achieve more reliability with consuming less power, turbo codes can be used as a powerful coding technique. On the other hand, to overcome the bandwidth constraint, a higher order modulation, such as M-PSK, may be needed. Heuristically it seems natural to use an encoding scheme whose symbol size is equal to the size of modulation symbols. In this paper we study the combination of mod-M turbo code with M-PSK modulation. Both cases of single input and multiple input encoders are considered. For the general case of multiple inputs, a decoding algorithm is formulated and its complexity is analyzed. Cases of M=4 and 8 are considered for simulation. The results show that there exists mod-M turbo codes which outperform the best known binary turbo codes, having the same complexity.