Since blast furnaces are generally controlled by operators, the minor faults regarded as disturbances might be contained in the collected data matrix. This can severely affect sample distributions, which leads to arbitrary fault detection results using traditional data-driven methods. In this paper, a novel fault detection method named robust principal component pursuit (PCP) to handle minor faults is proposed. The minor faults are separated from columns and rows, respectively, in the training matrix via two matrix norms. By applying the proposed robust PCP method, a low rank matrix containing important process information, as well as explicit variable relationships, and a block sparse matrix containing minor faults are derived. Moreover, the convergence of the proposed method is discussed. Hotelling's T-2 statistic is potentially useful for online process monitoring in the low rank matrix. Finally, to evaluate the decomposition capacity of the proposed method for a matrix containing minor faults, a comparison of the proposed method with other robust methods is presented. To test the effectiveness of the proposed method for fault detection, a numerical simulation is adopted at first. Finally, the power of the proposed method is illustrated in a real blast furnace process.