The large bandwidth available at 60 GHz together with the resulting wavelength of only 5 mm allow the design of multi-Gbps wireless devices equipped with large arrays of tiny antennas. This enables wireless communication of large contents multimedia such as high-definition video. However, due to the high cost and power consumption of analog frond-end (AFE) chains at 60 GHz, it is practically infeasible to allocate a dedicated AFE to each antenna. Thus, it is highly desirable to design low complexity multi-antenna architectures in which an analog linear transformation (ALT) is carried out in order to reduce the required number of AFE chains for digital spatial processing, while minimizing the capacity loss. In this paper, we propose a non-iterative algorithm for joint transmit/receive (TX/RX) ALT. The proposed algorithm is designed with the aim of maximizing the capacity of the resulting reduced dimension MIMO system, assuming a frequency selective propagation channel.