Correct.
This is one of those passages where the typical translations unfortunately do a nice job of clouding over the meaning of what is actually being talked about. It is not about women but wives, as the context makes clear. The Greek words for "men" and "women" can just as easily be translated "husbands" and "wives," and the only way to know which should be used is by closely analyzing the context. Here it is very clearly talking about married couples, as the following highlights will show you (note: I will save off correcting the translation of the passage for a later post).
1 Now I praise you, brethren, that you remember me in all things and keep the traditions just as I delivered them to you. 3 But I want you to know that the head of every man is Christ, the head of woman is man, and the head of Christ is God. 4 Every man praying or prophesying, having his head covered, dishonors his head. 5 But every woman who prays or prophesies with her head uncovered dishonors her head, for that is one and the same as if her head were shaved. 6 For if a woman is not covered, let her also be shorn. But if it is shameful for a woman to be shorn or shaved, let her be covered. 7 For a man indeed ought not to cover his head, since he is the image and glory of God; but woman is the glory of man. 8 For man is not from woman, but woman from man. 9 Nor was man created for the woman, but woman for the man. 10 For this reason the woman ought to have a symbol of authority on her head, because of the angels. 11 Nevertheless, neither is man independent of woman, nor woman independent of man, in the Lord. 12 For as woman came from man, even so man also comes through woman; but all things are from God. 13 Judge among yourselves. Is it proper for a woman to pray to God with her head uncovered? 14 Does not even nature itself teach you that if a man has long hair, it is a dishonor to him? 15 But if a woman has long hair, it is a glory to her; for her hair is given to her for a covering. 16 But if anyone seems to be contentious, we have no such custom, nor do the churches of God.