You need a Workbook_BeforeSave event procedure.

Alt+F11 to the VB Editor

Double-click on the ThisWorkbook object in the Project Explorer

Select Workbook from the left-hand dropdown and BeforeSave from the
right-hand dropdown at the top of the main window.

Insert the following between the lines that appear
(Private Sub Workbook_BeforeSave... and End Sub):

ThisWorkbook.Sheets("Sheet1").Range("A1") = Date

adjust the sheet name and cell address appropriately.

Bill Manville
MVP - Microsoft Excel, Oxford, England
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