For n = 1, 2 and 3, we construct a pair of transverse knots T1 and
, in the standard contact 3-sphere, satisfying the following properties:
(1) the topological knot type of T1 is the same as that of
,
(2) the self-linking number of T1 is equal to that of
,
(3)
is obtained from a transverse knot T2 by n stabilizations, and
(4) T1 is not transversely isotopic to
.