Delete named ranges from selection

If the recorder produces...

ActiveWorkbook.Names("MyName").Delete

...why then would the following fail with the goal being to remove all named ranges from a selection?

Sub DeleteNamedRange()

Dim rngCell As Range

   For Each rngCell In Selection
      ActiveWorkbook.Names(CStr(rngCell.Name)).Delete
   Next rngCell

End Sub

I'm receiving an 'Application or Object Defined Error' at line

ActiveWorkbook.Names(CStr(rngCell.Name)).Delete