Orthogonal conditional nonlinear optimal perturbations (O-CNOPs) is an important method for generating initial perturbations in ensemble forecasting. However, the traditional sequential optimization algorithm (S-CNOPs) for calculating O-CNOPs is computationally expensive. Subsequently, an efficient parallel algorithm for computing O-CNOPs (P-CNOPs) was proposed, but the initial implementation of this algorithm was based on the simple LORENZ-96 theoretical model. In this study, a more complex two-dimensional barotropic quasi-geostrophic model will be adopted to investigate the reliability and efficiency of P-CNOPs. The theoretical rationality of P-CNOPs will be demonstrated from both dynamical and algebraic perspectives. Numerical experiments show that P-CNOPs provide equivalent forecast skill to S-CNOPs ensemble forecasting, but the former has significantly higher computational efficiency than the latter, resulting in significant savings in computational resources. Therefore, P-CNOPs is a potentially efficient algorithm for computing O-CNOPs in complex models, and it is expected to be widely used in practical numerical weather prediction models in the future.