One of my friends wanted to married a sister but he changed his decision. He left her and married another sister. I did ask the first sister to marry me. Is there any wrong with my act of asking this sister for marriage and she was with my friend because I had big argument with this friend?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

If your friend proposed to marry the girl and her guardian accepted his proposal, then no one is permitted to propose to that girl until he, or she, or her guardian cancels the engagement. The Prophet said: “A believer is the brother of a believer, so it is not lawful for a believer to outbid his brother, and he should not propose an engagement when his brother has proposed until he gives up.”

Your friend marrying another woman is not a clear indication that he has given up the girl he first proposed to since it is possible that he intends to marry this girl also and live with two wives. As you know, one is allowed to marry up to four wives.
However, if your friend allows you to propose to this girl, or that he gives up and is no more interested in marrying her, or she or her guardian refuses his proposal, then you may make an offer of marriage. This ruling is derived from the Hadeeth that Faatimah bint Qays came to the Prophet and said: “Mu’aawiyah and Abu Jaham had asked for me in marriage. The Prophet did not deny it but proposed her to marry Usaamah.” [Muslim] She did not inform the Prophet about her acceptance to one of them. If she had informed him about her approval to one of them, he would not have suggested her to marry Usaamah. This is the preponderant opinion of Muslim scholars.

Allah knows best.