You problem is caused by deleting rows top to bottom. Try the other way round instead i.e.
Sub DelUnique()
Dim i As Integer
For i = Range("C" & Rows.Count).End(xlUp).Row To 2 Step -1
If Cells(i, 3) = "unique" Then
Rows(i).EntireRow.Delete
End If
Next
End Sub
Depending on how much data you have another option would be to use "Autofilter" with "unique" as criteria and then delete all the rows that matches in one go.
Alf