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Using unknotting number, we introduce a link diagram invariant of Hass andNowik type, which changes at most by 2 under a Reidemeister move.  As an application, we show that a certain infinite sequence of diagrams ofthe trivial two-component link need quadratic number of Reidemeister moves forbeing unknotted with respect to the number of crossings.  Assuming a certain conjecture on unknotting numbers of a certain series ofcomposites of torus knots, we show that the above diagrams need quadraticnumber of Reidemeister moves for being splitted.

Unknotting number and number of Reidemeister moves needed for unlinking