No Match formula that ignores when one cell is blank and other has data?

Just what the title says. I have a spreadsheet with duplicated columns (poor management by the person before me) but the data sometimes differs. I have a worksheet where I can paste both columns to check for mismatches, and research which entry is correct. The formula I am currently using is =IF(C2<>D2,"No match","")

How can I get the formula to ignore cases where one column has data, but the other is blank? For this application, that would be a false positive.

Thanks.