A big, diverse and balanced training data is the key to the success of deep neural network training. However, existing publicly available datasets used in facial landmark localization are usually much smaller than those for other computer vision tasks. A small dataset without diverse and balanced training samples cannot support the training of a deep network effectively. To address the above issues, this paper presents a novel Separable Batch Normalization (SepBN) module with a Cross-protocol Network Training (CNT) strategy for robust facial landmark localization. Different from the standard BN layer that uses all the training data to calculate a single set of parameters, SepBN considers that the samples of a training dataset may belong to different sub-domains. Accordingly, the proposed SepBN module uses multiple sets of parameters, each corresponding to a specific sub-domain. However, the selection of an appropriate branch in the inference stage remains a challenging task because the sub-domain of a test sample is unknown. To mitigate this difficulty, we propose a novel attention mechanism that assigns different weights to each branch for automatic selection in an effective style. As a further innovation, the proposed CNT strategy trains a network using multiple datasets having different facial landmark annotation systems, boosting the performance and enhancing the generalization capacity of the trained network. The experimental results obtained on several well-known datasets demonstrate the effectiveness of the proposed method.