Batch implementations of standard support vector machine (SVM) are inefficient on an online setting because they must be retrained from scratch every time the training set is modified (i.e., adding or removing some data samples). To solve this problem, Cauwenberghs and Poggio propose an incremental and decremental support vector classification algorithm (C&P algorithm). This paper proves the feasibility and finite convergence of the C&P algorithm through theoretical analysis. The feasibility ensures that each adjustment step in the C&P algorithm is reliable, and the finite convergence ensures that the C&P algorithm can converge to the optimal solution within finite steps. Finally, the conclusions of the theoretical analysis are verified by the experimental results.