A novel method for approximating transient growth in spatially evolving flows within the framework of local stability theory by using bi-orthogonality is presented. Although the local linear stability analysis is based on the parallel-flow assumption, it is able to accurately predict modal growth of discrete waves in boundary-layer flows using the \(e^n\) -method. However, the classical local approach fails for the concept of non-modal disturbances, where the growth is substantially under-predicted. In this study, it is shown that the prediction can be significantly improved by employing local adjoint stability solutions for a sequential downstream projection of the disturbances. While still using local theory with the parallel-flow assumption, this can be physically explained by the redistribution of energy between different scales, which appears to be one of the aspects of non-local disturbance growth. Results for the lift-up mechanism in a Blasius flow are presented and discussed.