Yongqian Xiang and his team members proposed a symmetric encryption algorithm based on double plaintext, named Bicycle algorithm. The block mode is ECB mode, and the encryption algorithm is based on a binary linear equations. There are some drawbacks in Bicycle algorithm, such as decryption failure due to the accuracy, invalid tamper proof module, unable to deal with the chosen plaintext attack and so on. In order to overcome these defects, we propose a new encryption algorithm called Re:Bicycle algorithm. Feistel network and three key encryption rules are introduced to rearrange the single group encryption structure. A more effective tamper proof function module is designed by using new parameters, and a CBC block mode based on double plaintext is designed to resist the chosen plaintext attack. Experiments show that the Re:Bicycle algorithm is better than the Bicycle algorithm in the overall efficiency.