Generalized spatial modulation (GSM) is a spectral-efficient technique used in multiple-input multiple-output (MIMO) wireless communications when the number of radio frequency chains at the transmitter is less than the number of transmit antenna elements. We propose a family of signal constellations, as an improvement over GSM, which splits the information bits into three parts, and encodes the first part into a set of complex symbols, the second part into the choice of a subset of antennas activated for transmission (as in GSM), and the third into a translation pattern that offsets the symbols transmitted through the activated antennas. The nominal coding gain (the ratio of the squared minimum distance between transmit vectors to the transmit power) of our scheme is higher than that of GSM by at least 0.86 dB, and this improvement can be as much as 2.87 dB based on the system parameters. We show that the new scheme has advantages over other known signal constellations for GSM, in terms of error performance, nominal coding gain and design flexibility.