Purpose: The generalized coherence factor (GCF), an adaptive beamforming technique, can reduce unnecessary signals from an unfocused position without reducing the contrast-to-noise ratio. However, the computational complexity of this method is large compared to the conventional delay-and-sum (DAS) beamformer. In the present paper, we propose a novel method to achieve the same reduction effect of unnecessary signals with a smaller computational load than that of the conventional GCF approach. Methods: One of the factors increasing the computational complexity of the GCF-based beamformer compared with DAS is the generation of analytic signals at receiving elements. We clarified the mechanism of generating unnecessary signal components to enable the calculation of the GCF value directly from real signals without generating analytic signals. Furthermore, we proposed a method to filter out these components without generating analytic signals. Results: The GCF values obtained using the proposed and conventional methods were compared and verified using the actual data acquired from a phantom with an ultrasound diagnostic system. We also compared the B-mode images. As a result, equivalent GCF values and similar B-mode image quality were achieved with the proposed method with reduced computational complexity. Conclusion: With the proposed method, generation of analytic signals at receiving elements can be omitted, and as a result, the computational load of the GCF method can be greatly reduced, while preserving the effect of reducing unnecessary signals like with the conventional method.