Flight Trajectory Prediction (FTP) is an essential task in Air Traffic Control (ATC), which can assist air traffic controllers to manage airspace more safely and efficiently. Existing approaches generally perform multi-horizon FTP tasks in an autoregressive manner, which is prone to suffer from error accumulation and low-efficiency problems. In this paper, a novel framework, called FlightBERT++, is proposed to i) forecast multi-horizon flight trajectories directly in a non-autoregressive way, and ii) improved the limitation of the binary encoding (BE) representation in the FlightBERT framework. Specifically, the proposed framework is implemented by a generalized Encoder-Decoder architecture, in which the encoder learns the temporal-spatial patterns from historical observations and the decoder predicts the flight status for the future time steps. Compared to conventional architecture, an extra horizon-aware contexts generator (HACG) is dedicatedly designed to consider the prior horizon information that enables us to perform multi-horizon non-autoregressive prediction. Additionally, a differential prediction strategy is designed by well considering both the stationarity of the differential sequence and the high-bits errors of the BE representation. Moreover, the Bit-wise Weighted Binary Cross Entropy loss function is proposed to optimize the proposed framework that can further constrain the high-bits errors of the predictions. Finally, the proposed framework is validated on a real-world flight trajectory dataset. The experimental results show that the proposed framework outperformed the competitive baselines.