Simple half-duplex repetition-based relaying protocols can achieve spatial diversity at the expense of additional relaying signals in the time domain. In this paper, a linear unitary precoder based on a singular vector for cooperative systems with the amplify-and-forward (AF) relaying protocol is proposed in order to improve spectral efficiency. An exact expression of the precoder design is first derived for the case of equal power allocation. Then, water-filling power allocation is used in conjunction with the precoder to further increase the system capacity, where the precoder matrix is generated with an iterative process. From the implementation point of view, the channel state information (CSI) has to be estimated and quantized in systems, the detail of which is described in the sequel. The adaptive modulation and coding (AMC) technique with the proposed precoder is also discussed to achieve high throughput performance. Finally, numerical and simulation results are presented to demonstrate the effectiveness of the proposed technique in improving capacity and throughput.