In the underlay decode-and-forward (DaF) cooperative cognitive radio (CR) network, an optimal relay can be selected by the conventional max-min selection on the condition of not violating the interference temperature (IT) constraint. However, the max-min selection may cause some extra amount of interference to the primary system (PS) such that the so-called transfer ratio (TR) may be lower. Note that TR is newly defined as the ratio of the secondary system's (SS's) capacity gain to the PS's capacity loss due to the activities of SS. In order to improve the TR value, we are motivated by the pricing function in game theory to propose a novel low-interference relay selection by taking the impacts of the interference from SS to PS into consideration. Using the low-interference selection, however, it will not always allow the optimal relay to be picked. To clarify this phenomenon, the still optimal probability is defined as the probability of selecting the optimal relay by the proposed scheme. In addition, the impacts of the low-interference selection on the SS's capacity and outage probability are also analyzed. The simulation results prove that compared with the max-min selection, the proposed scheme can achieve higher TR values as well as the total capacity which also indicates that a higher spectrum efficiency can be achieved. It is believed that the results of this paper can provide an alternative viewpoint of evaluating the spectrum efficiency and inspire more interesting and important research topics in the future.