  In this paper, we define a lassoing on a link, a local addition of a trivial
knot to a link. Let K be an s-component link with the Conway polynomial
non-zero. Let L be a link which is obtained from K by r-iterated lassoings. The
complete splitting number split(L) is greater than or equal to r+s-1, and less
than or equal to r+split(K). In particular, we obtain from a knot by r-iterated
component-lassoings an algebraically completely splittable link L with
split(L)=r. Moreover, we construct a link L whose unlinking number is greater
than split(L).
