Run macro upon value entered in B1 only if B1 > value in A1?

Maybe:

Private Sub Worksheet_Change(ByVal Target As Range)
    If Not Intersect(Target, Range("B1")) Is Nothing Then
        If Target.Value > Target.offset(, -1).Value Then Call MACROHERE
    End If
End Sub

Works! Thank you

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Using the code suggested above, it works fine except when I delete the value out of the cell - it throws up the Run-time error '13' Type Mismatch. Do you know why?

Try:

Private Sub Worksheet_Change(ByVal Target As Range)
    If Not Intersect(Target, Range("B1")) Is Nothing Then
        If Target.Value <> "" Then
        If Target.Value > Target.offset(, -1).Value Then Call MACROHERE
        End If
    End If
End Sub

I think it is reading "" as text.