An improved stage-specific multivariate calibration scheme is developed for multistage batch processes based on the covariance analysis unit. First, the process duration is automatically and properly divided into different stages, which reveals the changes of quality-related process correlation characteristics. The concept of stage-representative average process behaviour is then introduced, which is comprehensibly realized by averaging all covariance patterns within the same stage based on different weights. In this way, it stacks the cumulative effects of process variations on quality within each stage and meanwhile considers their time-varying characteristics. Subsequently, covariance-oriented OSC and variable selection are effectively combined, which can simplify the calibration model structure and enhance the causal relationship between predictors and quality by excluding the redundant latent factors and input variables. Finally, stage-representative PLS regression models are developed focusing on the critical-to-quality stages for online quality prediction. it shows that a complete multistage calibration solution is readily achieved from an "overall" stage perspective by smartly making use of covariance. The illustration study to injection molding shows the effectiveness of the proposed method for improving process comprehension and quality prediction.