except it be for fornication,
and shall marry another, committeth adultery: and whoso marrieth her which is put away doth commit adultery.
Your interpretation cannot be correct because it would conflict with Mark 10:11-12, Luke 16:18, and Cor. 10-11. "put away his wife, except it be for fornication" refers to a marriage that is not legitimate according to divine law such as a common law or incestuous marriage. See:
http://www.usccb.org/nab/bible/matthew/matthew5.htm#foot21 (Cath.)
http://catholicdefense.blogspot.com/2009/05/does-bible-permit-divorce-in-case-of.html (Cath.)
http://morechristlike.com/except-for-fornication-clause-of-matthew-19-9 (Prot.)