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• Lateral instability modes of vehicles on horizontal curves are discovered. • Boundary of each stability index is derived through calculation and analysis. • A theoretical framework for realizing a revised inferred design speed is established. • Previous speed limit strategies cannot fully guarantee the safety of driving. • Considerations in the application of the proposed method are demonstrated. An inferred design speed (IS) is the maximum vehicle speed for which all critical design speed-related criteria are met at a particular location, which is widely recognized as an important speed limit on highways. However, a side friction factor is used as an index for vehicle lateral stability in the calculation of IS for horizontal curves. This condition causes inaccuracies in the value of IS due to the incapability of the index in fully characterizing the steering stability and track-holding capability of vehicles. This paper aims to fill this gap by discovering the lateral instability modes of vehicles on horizontal curves and to determine the boundary of each index beyond which the corresponding mode of instability occurs. Thus, a theoretical framework for realizing a revised IS (RIS) was established. A high-precision seven-degree-of-freedom driver–vehicle–road mathematical model was developed using MATLAB/Simulink. The state of vehicle lateral instability on highway horizontal curves was decoupled, and the boundaries of vehicle stability indices were deduced using the theory of vehicle system dynamics. Accordingly, a procedure for determining RIS was proposed. Case studies were conducted on the three horizontal curves of a two-lane rural highway in China, and existing speed limit methods were compared with RIS. With in-depth consideration of the lateral instability characteristics of vehicles, RIS provides traffic management departments with a precise maximum safe speed on horizontal curves under various pavement friction conditions. It is expected to be a restriction with respect to safety for other speed limit strategies that consider driver expectancy and efficiency. [ABSTRACT FROM AUTHOR]