The square quadrature amplitude modulation (QAM) has been widely used for decades. Though it is not optimum in the sense of power efficiency, simple detection makes it in use for numerous digital communication systems deploying high-order modulation. In this paper, we propose new signal sets which make an effective use of limited power resource. We also suggest simple detection methods for the proposed signal sets to be meaningful from a point of view of implementation. The newly proposed constellations can provide advantages of 0.46 dB and 0.55 dB in signal-to-noise ratio over the square QAM in 16-ary and 64-ary signal sets while keeping low complexity for detection