Updating recent file list when vba saving a workbook

I have a short macro that saves files to a specific directory and filename based on values in the workbook. The problem is that the file list (I'm using Excel 2007) has the previous file name but not the current one. If I re-open the file using the recent documents short-cut, it will be a previous, obsolete version. Is there a way to make sure the recent documents updates when I save the file. Here's the macro:

Sub SaveAsExcel()
' Save the workbook as an .xlsm file
Dim fileSaveName As String
fileSaveName = Range("dirName") & Range("XLfileName")
ActiveWorkbook.SaveAs Filename:=fileSaveName, FileFormat:=xlOpenXMLWorkbookMacroEnabled, CreateBackup:=False
End Sub

Thanks.

XLA- thanks for the idea, but even after the file has been closed, it's still not showing up in the recent documents list of Excel. It is in Windows Explorer recent document list. But it's not picked up by Excel's recent document list.

Any other ideas?