Unique List 2 or more columns

Hi,
I'm trying to modify a code written by DonkeyOty that I found here:

HTML Code: 

Sub UniqueOrder() 
Dim LR As Long, i As Long
Dim xlCalc As XlCalculation
LR = Cells(Rows.Count, "C").End(xlUp).Row
With Application
    xlCalc = .Calculation
    .Calculation = xlCalculationManual
    .ScreenUpdating = False
    .EnableEvents = False
    For i = LR To 2 Step -1
        If .CountIf(Columns("C"), Cells(i, "C")) > 1 Then Rows(i).EntireRow.Delete
    Next i
    .Calculation = xlCalc
    .ScreenUpdating = True
    .EnableEvents = True
End With
End Sub

I have data in columns A and B, and I concatenated Columns A and B in column C, and used the code to make the unique list.
Is there a way this could be done without using column C?
I've attached a sample file.
Thanks,
Xrull