CORRECTED - Allergan licenses drug for night-time urination

(Corrects symptoms of overactive bladder in last paragraph)

* Allergan gets global rights to sell intra-nasal drug

* To pay privately held Serenity $43 mln upfront

* To make up to $122 mln in other future payments

NEW YORK, April 1 (Reuters) - Allergan Inc (AGN.N), broadening its urology product line, on Thursday said it had reached a deal with Serenity Pharmaceuticals LLC to develop and sell the privately held company's drug now in late-stage testing to treat frequent night-time urination.

Allergan, best known for its anti-wrinkle drug Botox, said the agreement gives it global rights to develop, manufacture and sell the nasally administered product, called Ser-120.

"Allergan will make an upfront payment to Serenity of $43 million, potential development and regulatory milestone payments of up to $122 million, future potential sales milestones, and royalty payments on worldwide sales," the companies said in a joint release.

The agreement includes all potential indications for the condition, formally known as nocturia, except pediatric bedwetting.

Nocturia often affects patients who have urologic conditions, such as overactive bladder and enlarged prostate, the companies said.

Allergan already sells a urology drug, called Sanctura, a once-daily drug to treat overactive bladder. That is a difficult-to-treat condition in which patients have a sudden and often unstoppable need to urinate. (Reporting by Ransdell Pierson, editing by Dave Zimmerman)