The man indeed ought not to cover his head, because he is the image and glory of God; but the woman is the glory of the man.
[1 Corinthians 11:7]

Context is important. St. Paul is speaking of a woman who is "praying or prophesying."

  5 But every woman praying or prophesying with her head not covered, disgraceth her head: for it is all one as if she were shaven.
 
 6 For if a woman be not covered, let her be shorn. But if it be a shame to a woman to be shorn or made bald, let her cover her head.