In this paper, we consider a device-to-device communication network in which $K$ transmitter-receiver pairs are sharing spectrum with each other. We propose a novel but simple binary scheduling scheme for this network to maximize the average sum rate of the pairs. According to the scheme, each receiver predicts its Signal-to-Interference-plus-Noise Ratio (SINR), assuming \emph{all} other user pairs are active, and compares it to a preassigned threshold to decide whether its corresponding transmitter to be activated or not. For our proposed scheme, the optimal threshold that maximizes the expected sum rate is obtained analytically for the two user-pair case and empirically in the general $K$ user-pair case. Simulation results reveal that our proposed SINR-threshold scheduling scheme outperforms ITLinQ \cite{navid}, FlashLinQ \cite{flash} and the method presented in \cite{G} in terms of the expected sum rate (network throughput). In addition, the computational complexity of the proposed scheme is $O(K)$, outperforming both ITLinQ and FlashLinQ that have $O(K^2)$ complexity requirements. Moreover, we also discuss the application of our proposed new scheme into an operator-assisted cellular D2D heterogeneous network.