Revenge Or Seeking Justice

I am fond of watching CSI(Crime Scene Investigation)-type of show on TV.  Not long ago, I watched a TV serial related to that theme in Chinese.  A policeman was stabbed to death while he was trying to stop a criminal committing a crime.   The criminal escaped.  All other officers in the the police department were very sad and vowed to catch the criminal.  It was a reasonable reaction given the situation.  However,  something started to irk me when I tried to digest the phrase, "avenge the murder of their colleague", coming out from one of the officers.  Would it be more appropriate if he said they would catch the criminal and bring the criminal to justice for the victim instead?