Paul didn't leave out a negative here as many think. He did not say, "Be not angry." He said, as it reads here, "BE ANGRY"—the actual Greek word is imperative, which is the usual form used for commands. We really have two imperatives in a row here: "Be angry" (orgizesthe); and "Do not sin" (hamartanete).
The first half of this verse is in all capitals in the NASB indicating that it is a quotation from the Tanakh. Paul is alluding to Psalm 4:4. So we need to answer this important question, "What does the Psalm mean?"
7/06/2014 - Pastor David B. Curtis - Berean Bible Church - http://www.bereanbiblechurch.org - Message# 713
View sermon transcript here: http://www.bereanbiblechurch.org/transcripts/ephesians/eph-04_26-27_be-angry_video.php