Error correcting output codes (ECOCs) have been proposed to improve the robustness of deep neural networks (DNNs) against hardware defects of DNN hardware accelerators. Unfortunately, existing efforts suffer from drawbacks that would greatly impact their practicality: 1) robust accuracy (with defects) improvement at the cost of degraded clean accuracy (without defects); 2) no guarantee on better robust or clean accuracy using stronger ECOCs. In this paper, we first shed light on the connection between these drawbacks and error correlation, and then propose a novel comprehensive error decorrelation framework, namely COLA. Specifically, we propose to reduce inner layer feature error correlation by 1) adopting a separated architecture, where the last portions of the paths to all output nodes are separated, and 2) orthogonalizing weights in common DNN layers so that the intermediate features are orthogonal with each other. We also propose a regularization technique based on total correlation to mitigate overall error correlation at the outputs. The effectiveness of COLA is first analyzed theoretically, and then evaluated experimentally, e.g. up to 6.7% clean accuracy improvement compared with the original DNNs and up to 40% robust accuracy improvement compared to the state-of-the-art ECOC-enhanced DNNs.