Paul and Barnabas stayed together, preaching the Gospel, until John Mark decided to go home in the middle of a missionary journey. This angered Paul, and Paul decided that he didn't want to take John Mark with him again. On a later missionary journey Barnabas asked Paul to give John Mark another chance, and Paul refused:

(Acts 15:35-40 KJV) "Paul also and Barnabas continued in Antioch, teaching and preaching the word of the Lord, with many others also. {36} And some days after Paul said unto Barnabas, Let us go again and visit our brethren in every city where we have preached the word of the Lord, and see how they do. {37} And Barnabas determined to take with them John, whose surname was Mark. {38} But Paul thought not good to take him with them, who departed from them from Pamphylia, and went not with them to the work. {39} And the contention was so sharp between them, that they departed asunder one from the other: and so Barnabas took Mark, and sailed unto Cyprus; {40} And Paul chose Silas, and departed, being recommended by the brethren unto the grace of God."

John Mark was actually Barnabas' nephew:

(Colossians 4:10 KJV) "Aristarchus my fellow prisoner saluteth you, and Marcus, sister's son to Barnabas, (touching whom ye received commandments: if he come unto you, receive him;)"

This caused division between Paul and Barnabas so that Paul went out with Silas instead of Barnabas. Paul would later forgive John Mark and accept him back into the fold as a fellow missionary.

(2 Timothy 4:11 KJV) "Only Luke is with me. Take Mark, and bring him with thee: for he is profitable to me for the ministry."