  It is known that the naive Abelian Wilson loop defined by the Abelian
projection cannot reproduce the correct behavior of the double-winding Wilson
loop. It is also known that the naive Abelian Wilson loop cannot reproduce the
correct behavior of the Wilson loops in higher representations, but this
problem was recently solved by using the redefined "Abelian" Wilson loop. In
this talk, we will give another reason why this redefined "Abelian" Wilson loop
behaves correctly, and by following the same line of the argument, we will
propose redefined "Abelian" double-winding Wilson loop which is considered to
behave correctly.
