Abstract: Orthogonal conditional nonlinear optimal perturbations (O-CNOPs) represent an important method for generating initial perturbations in ensemble forecasting. However, the traditional sequential optimization algorithm for calculating O-CNOPs (S-CNOPs) is computationally expensive. Therefore, an efficient, parallel algorithm for computing O-CNOPs (P-CNOPs) is proposed, but the initial implementation of this algorithm is based on the simple LORENZ-96 theoretical model. In this study, a more complex, two-dimensional barotropic quasi-geostrophic model is adopted to investigate the reliability and efficiency of P-CNOPs. The theoretical rationality of P-CNOPs is demonstrated from the dynamical and algebraic perspectives. Numerical experiments show that P-CNOPs provide equivalent forecast skill to S-CNOPs ensemble forecasting, but the former has considerably higher computational efficiency than the latter, resulting in notable 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.