Minutes: noun an official and legal record of the proceedings of a meeting, conference, convention, etc.
Minutes are a legal record of what was done at a meeting--not necessarily what was said. Well written agendas help lead to well written minutes.
Use your agenda as an outline to write minutes. Every board meeting includes a vote to accept the minutes from the previous meeting.
Here's one template from Microsoft's Word Documents library. There are others you may find more useful.
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Minutes are not a transcript of the meeting, but a "record or summary of all motions, proposals, resolutions, and any other matter formally voted upon and the vote thereon." If a vote was not unanimous, the minutes must show how each Board member voted on an action. (Public Officers Law Subsection 87 [3] [a].
Start by noting the date/time of the meeting as well as attendance. You should refrain from including quotes and play-by-play narratives. The tone should be neutral.
Example: FLLS Board meeting minutes https://www.flls.org/board-of-trustees/ (Click link and scroll down to see minutes)
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Typically, the board secretary records the minutes.
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If your Board takes a formal vote on any action during executive session, then yes. The minutes should reflect a record or summary of the final determination of such action, and the date and vote thereon provided should be included in the minutes. However, the summary need not include matters which are not required to be made public by the Freedom of Information Law. Remember, meeting minutes are meant to be shared.
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Minutes are FOIL-able records, so it is recommended to keep them indefinitely. For more information on records retention see Retention and Disposition Schedules | New York State Archives
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Yes, a draft of your meeting minutes must be posted to your library's website within two weeks of the meeting. This is required by law. The fact that it is a "draft" is fine. Technically, they are not accepted until voted on at your next Board meeting.