How Do I stop this macro from running if there is an error?

Assign the result of the search to a range variable and test if there is anything there:

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Thank you for your quick response. However I am getting a Run-Time error '13': Type Mismatch. Any suggestions how to correct this?

On which line? Does this work?

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It kind-of works, but when the code is run it deletes the row where the 'NAME' was defined, which is a different sheet. I would like it to delete the row on the data sheet where it found the match.

I would have thought it should do that. This is where you attach a workbook.

I added the code below after defining 'NAME' and that seems to have corrected:

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So full code reads:

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Rows(r.Row).Delete Shift:=xlUp

Your problem was stemming from this line. You were seaching for the row and your data sheet but THEN the line above was telling it to remove the Row on the currenlty active sheet.

Here's this line corrected so that it removes from the data sheet ... even if the data sheet is not the active sheet.

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Sorry, wasn't paying attention. Either a sheet reference or nimrod's approach will sort it out.