IN 1994, Calvin Klein designed a fragrance that embodied, in its flat little screw-top bottle, the disaffected, sexually ambivalent grunge youth of the moment. CK One, with its unconventional black and white advertisements filled with moping, androgynous models, was arguably the most perfectly tailored fragrance ever pitched to one market, breaking industry rules and records, selling 20 bottles per minute at its peak. A unisex brand that became the olfactory talisman of Generation X, CK One was so authentically grunge it was carried in record stores alongside albums by Nirvana.

Next month, Calvin Klein Inc. and Coty, its fragrance licensee, will introduce a sequel to CK One for a new generation, the so-called millennials, and in doing so, they will attempt to capture lightning in a bottle for a second time. Calvin Klein, now without its namesake designer, hopes to rejuvenate a fragrance embodying the essence of hip 20-somethings — even at the risk that such a notion is as outdated as a Prince song about partying like it’s 1999.

There are reasons to ask whether the Calvin Klein company can repeat its CK One success. The beauty industry has been in a slump for several years, facing a decline that is in part the result of young consumers spending more money on electronics than on fashion and fragrances. CK One offshoots — CK Be, introduced in 1996; several limited-edition bottle designs since 2000; and a fruitier CK One remix from the summer of 2004 — served as little more than stopgaps in the decline of a brand that, to today’s young adults, is as antiquated as shopping for music in a record store.

CK One, which had annual sales of about $90 million in the mid-1990s, now sells about $30 million in the United States, its reign having ended around the time Mr. Klein sold his company to Phillips-Van Heusen in 2002 and stepped back from daily involvement. Added to its other challenges, the Calvin Klein company is trying to develop a hit fragrance without the era-defining instincts Mr. Klein displayed in the days when he hired Brooke Shields to sell bluejeans. The only major figure to carry over from the creation of the original scent is Ann Gottlieb, a fragrance consultant and the nose of Calvin Klein since the designer started making scents in 1985. She described the concepts of CK One and its sequel “as different as red and yellow.”