This paper introduces a new surface-hopping method, QTSH-XF, which combines the nuclear equation from quantum trajectory surface-hopping (QTSH) with the electronic equation from the exact factorization approach (SHXF). The method eliminates three ad hoc aspects of traditional surface-hopping algorithms: velocity rescaling, energy conservation at the trajectory level, and internal inconsistency. QTSH-XF is shown to accurately simulate non-adiabatic dynamics in Tully models and a linear vibronic coupling model of the photo-excited uracil cation. Surface-hopping is a powerful method for simulating non-adiabatic dynamics in large molecules, but its reliability is reduced by ad hoc velocity adjustments and decoherence corrections. QTSH-XF addresses these issues by combining the nuclear equation from QTSH with the electronic equation from SHXF, resulting in a more robust method that retains the computational efficiency of independent-trajectory methods. The method is based on the exact factorization approach, which provides a first-principles description of decoherence. QTSH-XF eliminates the need for velocity rescaling and energy conservation at the trajectory level, while maintaining the practical efficiency of independent-trajectory methods. The method is shown to accurately capture decoherence and energy conservation in both Tully's extended coupling region (ECR) model and a linear vibronic coupling model of the uracil cation. QTSH-XF is compared with other surface-hopping methods, including SHXF and QTSH, and is shown to provide more accurate results in terms of energy conservation and internal consistency. The method is also shown to be more efficient than traditional SH methods, as it eliminates the need for velocity rescaling and hop rejection. The results demonstrate that QTSH-XF provides a more accurate and reliable simulation of non-adiabatic dynamics in complex systems.This paper introduces a new surface-hopping method, QTSH-XF, which combines the nuclear equation from quantum trajectory surface-hopping (QTSH) with the electronic equation from the exact factorization approach (SHXF). The method eliminates three ad hoc aspects of traditional surface-hopping algorithms: velocity rescaling, energy conservation at the trajectory level, and internal inconsistency. QTSH-XF is shown to accurately simulate non-adiabatic dynamics in Tully models and a linear vibronic coupling model of the photo-excited uracil cation. Surface-hopping is a powerful method for simulating non-adiabatic dynamics in large molecules, but its reliability is reduced by ad hoc velocity adjustments and decoherence corrections. QTSH-XF addresses these issues by combining the nuclear equation from QTSH with the electronic equation from SHXF, resulting in a more robust method that retains the computational efficiency of independent-trajectory methods. The method is based on the exact factorization approach, which provides a first-principles description of decoherence. QTSH-XF eliminates the need for velocity rescaling and energy conservation at the trajectory level, while maintaining the practical efficiency of independent-trajectory methods. The method is shown to accurately capture decoherence and energy conservation in both Tully's extended coupling region (ECR) model and a linear vibronic coupling model of the uracil cation. QTSH-XF is compared with other surface-hopping methods, including SHXF and QTSH, and is shown to provide more accurate results in terms of energy conservation and internal consistency. The method is also shown to be more efficient than traditional SH methods, as it eliminates the need for velocity rescaling and hop rejection. The results demonstrate that QTSH-XF provides a more accurate and reliable simulation of non-adiabatic dynamics in complex systems.