In this paper, performance in terms of Bit Error Rate (BER) and Frame Error Rate (FER) of multi binary turbo codes (MBTC) over Nakagami frequency nonselective fading channels are presented. The proposed MBTCs consist of the parallel concatenation of two identical 2/3-rate recursive systematic, convolutional (RSC) double binary codes. We choose to model the channel fading with Nakagami-m distribution since it fits well to the empirical fading data of the current wireless transmission systems. The simulation results show that the MBTCs outperform the classical turbo codes for low-targeted FER (around 10e-4) since their error-floor is negligible.