[excel] Delete all duplicate rows Excel vba

I have a worksheet with two columns: Date and Name. I want to delete all rows that are exact duplicates, leaving only unique values.

Here is my code (which doesn't work):

Sub DeleteRows()

Dim rng As Range
Dim counter As Long, numRows As Long

With ActiveSheet
    Set rng = ActiveSheet.Range("A1:B" & LastRowB)
End With
numRows = rng.Rows.Count

For counter = numRows To 1 Step -1
    If rng.Cells(counter) Like rng.Cells(counter) - 1 Then
        rng.Cells(counter).EntireRow.Delete
    End If
Next

End Sub

It's "Like rng.Cells(counter)-1" that seems to be the cause- I get "Type Mismatch".

The duplicate values in any column can be deleted with a simple for loop.

Sub remove()
Dim a As Long
For a = Cells(Rows.Count, 1).End(xlUp).Row To 1 Step -1
If WorksheetFunction.CountIf(Range("A1:A" & a), Cells(a, 1)) > 1 Then Rows(a).Delete
Next
End Sub