Currently, people use online social media such as Twitter or Facebook to share their emotions and thoughts. Detecting and analyzing the emotions expressed in social media content benefits many applications in commerce, public health, social welfare, etc. Most previous work on sentiment and emotion analysis has only focused on single-label classification and ignored the co-existence of multiple emotion labels in one instance. This paper describes the development of a novel deep learning-based system that addresses the multiple emotion classification problem in Twitter. We propose a novel method to transform it to a binary classification problem and exploit a deep learning approach to solve the transformed problem. Our system outperforms the state-of-the-art systems, achieving an accuracy score of 0.59 on the challenging SemEval2018 Task 1:E-cmulti-label emotion classification problem.