This claim rests on the same general basis as that which is made concerning the instances in the Gospels in which Jesus is depicted as angry (Note - see that page also for the textual issue surrounding Matthew 5:22). Both stem from the mistaken assumption that Matthew 5:22 condemns ALL anger. This is not, however, the case. Look at Matthew 5:22 below,
"But I say unto you, That whosoever is angry with his brother without a cause shall be in danger of the judgment...."
Note that this passage condemns UNJUST anger, anger which stems not from any legitimate grievance, but instead from envy and self-interest, just the sort of emotions which are likely to cause a person to become bitter and angry with another for no real reason. As was noted in the other response, concerning Jesus' anger, there are times when anger can be justified, and even be an appropriate response. This is exemplified by the Lord's anger, which was other-centred, not self-centred, and was directed against those who were perpetrating injustice against the weak, poor, and helpless, and were therefore profaning God's name.
The passage in Ephesians, then, cannot be said to be contradictory to the TRUE reading of Matthew 5:22. Ephesians 4:26 says,
"Be ye angry, and sin not: let not the sun go down upon thy wrath."
This verse, found in a passage which relates a whole series of teachings on the proper behaviour of a Christian, is an expansion on the doctrine of righteous anger, and teaches how such anger should be governed in our behaviour. Anger should not only be just, i.e. had for the right reason (other-centred, unselfish), but also must be expressed rightly by not allowing the anger to control you to the extent that it causes you to sin. For instance, even if a Christian is rightly angry about an injustice which another person has suffered, this Christian should not allow that anger to cause them to use foul language, seek personal revenge, etc. Further, anger is not to be allowed to dominate the thought life and personality of a Christian, and hence, should not be retained for an inappropriate amount of time (figuratively described as "the sun going down", i.e. retaining it overnight once the injustice is past).
Thus, we see that the entire claim to contradiction rests on faulty reading of Matthew 5:22, and isn't a contradiction at all.