This paper presents a new data-driven fault detection method called covariance eigenpairs neighbour distance (CEND) for monitoring chemical processes. It processes measured data in one-step sliding windows to estimate covariance, and the eigenpairs of each sample covariance matrix are recursively calculated using rank-one modification. The eigenvalues and selected elements of eigenvectors are stacked into reference vectors. For each window data containing the latest measurement vector, the neighbour distance of eigenpairs from the reference matrix can be effectively calculated by virtue of k-d tree. The neighbour distance serves as the detection index, whose control limit can be determined by validation dataset with assigning a significance level. A high neighbour distance exceeding the control limit implies the occurrence of fault. Simulations on the continuous stirred tank reactor (CSTR) and the Tennessee Eastman process (TEP) both indicate the superior fault detectability of the proposed method, compared with conventional multivariate statistical process monitoring (MSPM) methods such as principal component analysis (PCA) and independent component analysis (ICA).