Full-duplex (FD) communication has been shown to provide an increased achievable rate, while millimeter wave (mmWave) communications benefit from a large available bandwidth that further improves the achievable rate. On the other hand, the concept of multi-set space-time shift keying (MS-STSK) has been proposed to provide a flexible design trade-off between throughput and performance. Hence, in this work, we consider the design of an FD-aided MS-STSK transceiver for millimeter wave communications. However, a major challenge is that channel reciprocity is not valid in mmWave communications due to shorter channel coherence time. Thus, the uplink (UL) pilots cannot be utilized to estimate the downlink (DL) channel. To overcome this challenge, we propose a beamforming technique based on channel statistics without assuming channel reciprocity. For this purpose, a closed-form expression for the outage probability of the system is derived by employing the characterization of the ratio of the Indefinite Quadratic Form (IQF). The derived analytical expression is then utilized to design optimum beamforming weights using the Sequential Quadratic Programming (SQP)-based heuristic method. Moreover, an Iterative Statistical Method (ISM) of joint transmit and receive beamforming algorithm is also developed by utilizing Principle Eigenvector (PE) and Generalized Rayleigh Quotient (G-RQ) optimization techniques. Finally, we verify our simulation results with the theoretical analysis.