The paper introduces a new surface-hopping method, denoted as QTSH-XE, which combines the nuclear equation from quantum trajectory surface-hopping (QTSH) with the electronic equation derived from exact factorization. This approach eliminates the need for ad hoc velocity adjustments and decoherence corrections, making it more reliable and physically sound. The method is tested on Tully's extended coupling region (ECR) model and a linear vibronic coupling model of the photo-excited uracil cation, demonstrating its ability to capture non-adiabatic dynamics accurately. The results show that QTSH-XE outperforms traditional surface-hopping methods in terms of energy conservation and internal consistency, while retaining the computational efficiency of independent-trajectory methods. The paper also discusses the performance of different variants of QTSH-XF, including the impact of velocity rescaling and the introduction of a quantum-momentum-driven force term. Overall, the proposed method provides a robust and physically motivated approach to simulate non-adiabatic dynamics in large molecules.The paper introduces a new surface-hopping method, denoted as QTSH-XE, which combines the nuclear equation from quantum trajectory surface-hopping (QTSH) with the electronic equation derived from exact factorization. This approach eliminates the need for ad hoc velocity adjustments and decoherence corrections, making it more reliable and physically sound. The method is tested on Tully's extended coupling region (ECR) model and a linear vibronic coupling model of the photo-excited uracil cation, demonstrating its ability to capture non-adiabatic dynamics accurately. The results show that QTSH-XE outperforms traditional surface-hopping methods in terms of energy conservation and internal consistency, while retaining the computational efficiency of independent-trajectory methods. The paper also discusses the performance of different variants of QTSH-XF, including the impact of velocity rescaling and the introduction of a quantum-momentum-driven force term. Overall, the proposed method provides a robust and physically motivated approach to simulate non-adiabatic dynamics in large molecules.