procedure TForm1.Button1Click(Sender: TObject);
begin
  With TStringList.Create() do
  begin
    Duplicates := dupIgnore;
    Sorted := True;
    AddStrings(Memo1.Lines);
    Memo1.Clear();
    Memo1.Text := Text;
    Free();
  end;
end;

var
i:integer;
begin
i:=0;
while i < form1.Memo1.Lines.Count do
begin
if form1.Memo1.Lines.IndexOf(form1.Memo1.Lines[i]) < i then
form1.Memo1.Lines.Delete(i)
else
inc(i);
end;
end;