Due to high spectral efficiency, immunity to frequency selective fading, and high data rate, OFDM became a popular modulation technique in digital communication systems. Effectiveness of a signal constellation used in a communication system can provide a fundamental basis for efficiency of application networks. During recent years, different constellations were designed for different modulation schemes. In this research, two new triangular constellations schemes which are named as TRI1 and TRI2 are introduced to replace for the well-known rectangular QAM constellation in OFDM modulation. In this paper, the new proposed schemes are compared with different triangular constellations. It has been shown that these new schemes have three major advantages with respect to the QAM. The first advantage is its lower BER which results from the better usage of the constellation space with longer minimum distances. The second advantage of these schemes is their lower PAR with respect to the rectangular QAM constellation. The third property, as the last advantages, is their higher noise immunity with respect to the commonly used QAM constellation. Both mathematical analysis and simulation results demonstrate that by applying high fading channels with AWGN and ISI impairment simultaneously, the TRI1 and TRI2 exhibit a superior performance compared to the rectangular QAM. As a result, they are good choice for high speed and real-time multicarrier applications such as DAB, DVB, and WiFi at no extra cost. Manuscript profile