1 Corinthians 11:15
But if a woman have long hair, it is a glory to her: for [her] hair is given her for a covering.
Note 13 at 1Co 11:15: This verse is teaching that a woman's long hair is equivalent to a covering or veil. Therefore, a woman with long hair has no further need to wear some piece of cloth for a covering; her hair is her covering. Likewise, a man with short hair is uncovered, conforming to the custom recited in these verses.
With this in mind, we can go back to some of the previous verses in this chapter and read them with new meaning. 1Co 11:4 is saying that a man who prays or prophesies with long hair is dishonoring Christ. In 1Co 11:5, a woman who prays or prophesies with short hair is dishonoring her husband, just as if she were shaved bald. In 1Co 11:6, if it is a shame for a woman to be bald, then let her keep her hair long.
It must be remembered that these were customs of Paul's day that had been in place for centuries and still exist in many cultures to this present day. Paul was neither approving nor rejecting this custom. He simply used it to illustrate that God, not man, was their spiritual authority (see note 14 at 1Co 11:16).