This is how
Deuteronomy 24:1-4 reads in the Dead Sea scrolls:
1 If a man takes a wife and marries her, but she finds no favor in his eyes because he has found something objectionable about her, then he shall write her a bill of divorce and put it in her hand and send her from his house. 2 She may then go and be another man’s wife, 3 And if the latter husband who took her to be his wife dislikes her and writes her a bill of divorce and puts it in her hand and sends her from his house, or if the latter husband who took her to be his wife dies, 4 her former husband who had sent her away, cannot take her again to be his wife after she has been defiled. For that is an abomination before the Lord; you shall not bring sin upon the land which the Lord your God is giving you.
The Septuagint, some times called the LXX, is the ancient Greek version of the Hebrew Scriptures translated by a number of different Jewish scholars over the course of the third, second, and first centuries BC. The LXX was the Scriptures that the Apostles used in their writings which became our New Testament. Here is how
Deut 24:1-4 reads in the LXX (Apostolic Bible Polyglot First Edition copyright 1996)
1 And if any take a woman and should live with her, and it shall be if she should not find favor before him, for he finds in her an indecent thing, then he shall write to her a certificate of divorce scroll, and he shall put it into her hands and he shall send her from out of his house. 2 And going forth, should she become another man’s wife, 3 and the last husband should detest her, and should write to her a certificate of divorce scroll, and he should put it into her hands, and send her from out of his house or her last husband should die who took her to himself as wife; 4 the former husband sending her out shall not be able to return to take her to himself for a wife after her being defiled; for it is an abomination before the Lord your God, and you shall not defile the land which the Lord your God gives to you by lot.
The Complete Apostle’s Bible, copyright 2003 uses the term “unbecoming thing” instead of “indecent thing” like the version above.
As Hebrew became more unfamiliar with people, it became the custom for a person to give a paraphrase in Aramaic for the Scripture that had been read aloud in Hebrew. This paraphrase was called a Targum. Something like this took place in
Nehemiah 8:1-8. At first a targum could not be written down but memorized. Later they were written out. Here is how a targum of
Deuteronomy 24:1-4 reads. Note that the verses are not numbered:
When a man hath taken a wife and gone unto her, if she hath not favour in his eyes because he findeth the thing that is wrong in her, then he may write her a bill of divorce before the court of justice, and put it into her power, and send her away from his house. And departing from his house she may go and marry another man. But should they proclaim from the heavens about her that the latter husband shall dislike her, and write her a bill of divorce, and put it into her power to go from his house; or should they proclaim about him that lie the latter husband shall die: it shall not be in the power of the first husband who dismissed her at the beginning to return and take her to be with him as his wife, after that she hath been defiled; for that is an abomination before the Lord: for the children whom she might bear should not be made abominable, or the land which the Lord your God giveth you to inherit become obnoxious to the plague.
The above three readings can give us an idea of how the Jewish people understood what is called
Deuteronomy 24:1-4 in our Bibles around the time of the establishment of the New Testament Church. In each case divorce was permitted if the husband found something “objectionable about her” (Dead Seas Scroll), or “an indecent thing” (LXX), or “an unbecoming thing” (LXX) or “a thing that is wrong” (Targum). This would not be divorce because of adultery because the penalty for that was death. This “unbecoming thing” had become pretty loose interpreted around the first century BC and AD and divorce was allowed if the man found someone he liked better or if the wife’s voice could be heard by the neighbors or basically if the husband felt like something was the matter with her.
The following is from a current Jewish version of the Old Testament
Deuteronomy 24
Jewish Publication Society Tanakh (1917)
1 When a man taketh a wife, and marrieth her, then it cometh to pass, if she find no favour in his eyes, because he hath found some unseemly thing in her, that he writeth her a bill of divorcement, and giveth it in her hand, and sendeth her out of his house, 2 and she departeth out of his house, and goeth and becometh another man's wife, 3 and the latter husband hateth her, and writeth her a bill of divorcement, and giveth it in her hand, and sendeth her out of his house; or if the latter husband die, who took her to be his wife; 4 her former husband, who sent her away, may not take her again to be his wife, after that she is defiled; for that is abomination before the LORD; and thou shalt not cause the land to sin, which the LORD thy God giveth thee for an inheritance.
I just included these verses to show that the Jewish people and therefore the early Christians had a more liberal view of divorce and remarriage than many of us have today.
My soul followeth hard after thee....Love one another with a pure heart fervently. 
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