Process monitoring based on neural networks is getting more and more attention. Compared with classical neural networks, high-order neural networks have natural advantages in dealing with heteroscedastic data. However, high-order neural networks might bring the risk of overfitting and learning both the key information from original data and noises or anomalies. Orthogonal constraints can greatly reduce correlations between extracted features, thereby reducing the overfitting risk. This paper proposes a novel fault detection method called second-order component analysis (SCA). SCA rules out the heteroscedasticity of pro-cess data by optimizing a second-order autoencoder with orthogonal constraints. In order to deal with this constrained optimization problem, a geometric conjugate gradient algorithm is adopted in this paper, which performs geometric optimization on the combination of Stiefel manifold and Euclidean manifold. Extensive experiments on the Tennessee-Eastman benchmark pro-cess show that SCA outperforms PCA, KPCA, and autoencoder in missed detection rate (MDR) and false alarm rate (FAR).