An anti-lock braking system (ABS) is widely used these days as a technology for improving vehicle safety by maintaining braking performance so as to provide accident avoidance capability. Papers continue to be published about ABS today even though considerable time has passed since it became commonplace on vehicles. One aspect that especially attracts interest is the control method based on the slope of the mu-lambda curve. The notation mu here is called the brake friction coefficient, a value that is obtained by dividing the brake force by the tire load. The notation lambda expresses the slip ratio in the direction of tire rotation. The brake friction coefficient mu is a nonlinear function of the slip ratio lambda, and the curve of this function is referred to as the mu-lambda curve. The slope of the mu-lambda curve represents the ratio between the rate of change in the slip ratio and the rate of change in the brake friction coefficient. The slope of the mu-lambda curve, which is referred to here as the mu slope for short, is known to provide effective information for braking control, but its use still remains at the research level owing to a problem in estimating its value with sufficient accuracy. The authors have found that tire hysteresis is a major factor that causes estimation accuracy to decrease. Hysteresis here refers to differences in the brake friction coefficient when the slip ratio increases or decreases. Previously, Shimizu et al. investigated the relationship between hysteresis and the tire tread. However, the above-mentioned knowledge about hysteresis was applied for the first in the present study to the estimation of the mu slope. The results of vehicle tests showed that estimation accuracy was substantially improved with this method. This paper is organized as follows. First, a method of estimating the brake force is explained, as this indicated by the title of this paper, a brake torque sensor was used to obtain data for calculating the brake force. An explanation is then given of the conventional approach to estimating the mu slope using the fixed trace method. This method provides the foundation of a revised method of estimating the mu slope, which is discussed as the main subject of this paper. The use of the mu slope in variable control of the target slip ratio is then explained. Finally, the results obtained in vehicle tests with this slip ratio control procedure are presented to show the effectiveness of this revised method of estimating the mu slope.