This paper proposes an EEG-based Brain-Machine Interface (BMI) system such that 1) the machine can determine when to end the learning phase automatically by monitoring the learning progress using the Sequential Error Rate (SER) as an evaluation index and 2) it involves sequential learning in both the brain and the machine in a cooperative manner. In the proposed 'Brain-Machine Co-learning', subjects learn how to use the system by means of real-time visual feedback, whereas the machine learns the subjects' EEG signals by Bayesian sequential learning. The SER refers to the average classification error rate windowed over a short time period, and it represents the status of Bayesian sequential learning in real time. In our proposed approach, subjects can use the system while eliminating unnecessary training. The proposed system was tested against an SSVEP classification problem. The training phase varied for each subject and was sometimes short, yet satisfactory, leading to high classification accuracy.