This study presents a novel method for achieving chiral transmission in a non-Hermitian system using an open evolution trajectory, which does not require a closed path. The research demonstrates high-efficiency chiral transmission between eigenmodes localized in individual waveguides. The key mechanism is the non-adiabatic jump (NAJ), which occurs during the evolution process and enables the chiral response. The system is implemented in a coupled silicon waveguide system at telecommunication wavelengths, showing high transmission efficiency. The proposed open trajectory utilizes the same asymptotic eigenmodes at infinite points, which are not symmetrical or anti-symmetrical modes in PT- or anti-PT-symmetric systems. This approach avoids path-dependent losses and reduces fabrication complexity compared to previous methods that rely on closed trajectories. The results show that the system can achieve high-efficiency chiral transmission between modes [1,0]^T and [0,1]^T, with the output state depending on the evolution direction. The study also highlights the potential applications of this method in optical devices and quantum information processing. The experimental results confirm the theoretical predictions, demonstrating the effectiveness of the open trajectory in achieving chiral transmission with high efficiency.This study presents a novel method for achieving chiral transmission in a non-Hermitian system using an open evolution trajectory, which does not require a closed path. The research demonstrates high-efficiency chiral transmission between eigenmodes localized in individual waveguides. The key mechanism is the non-adiabatic jump (NAJ), which occurs during the evolution process and enables the chiral response. The system is implemented in a coupled silicon waveguide system at telecommunication wavelengths, showing high transmission efficiency. The proposed open trajectory utilizes the same asymptotic eigenmodes at infinite points, which are not symmetrical or anti-symmetrical modes in PT- or anti-PT-symmetric systems. This approach avoids path-dependent losses and reduces fabrication complexity compared to previous methods that rely on closed trajectories. The results show that the system can achieve high-efficiency chiral transmission between modes [1,0]^T and [0,1]^T, with the output state depending on the evolution direction. The study also highlights the potential applications of this method in optical devices and quantum information processing. The experimental results confirm the theoretical predictions, demonstrating the effectiveness of the open trajectory in achieving chiral transmission with high efficiency.