Can you read code?
As written it stops when it hits an empty cell.
It ran fine for me on contiguous data. (which was my assumption since you
stated no conditions).
This should work with data that contains empty cells:
Sub bbbb()
Dim rng As Range
Set rng = Cells(Rows.Count, 1).End(xlUp)
Do While Not rng.Row = 1
If Not IsEmpty(rng) Then
If Application.CountIf(Range(Cells(1, 1), _
Cells(rng.Row, 1)), Cells(rng.Row, 1)) > 1 Then
rng.ClearContents
End If
End If
Set rng = rng.Offset(-1, 0)
Loop
End Sub