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New York’s American Museum of Natural History has many exhibits of taxidermy under glass: a mule deer; a wolverine; even some miniature mastodons. On Monday night, however, the museum put something else on display – a case study in how to get another season of your show on the air when the current one hasn’t completed its arc.

In unveiling the fourth season of the much-buzzed about series “Girls” to a big crowd of well-wishers and celebrities, HBO programming president Michael Lombardo let slip that he had already approved a fifth season of the show. The reason, he said, was that the series continued to operate at such a high level of quality that he saw no reason not to let it continue.

As things turn out, “Girls” creator and producer Lena Dunham and producer Jenni Konner made part of their pitch for the next cycle of the series while on a plane with HBO executives. “It was like a flying cocktail party,” said Konner, addressing the assembly. Dunham and Konner said they had already written the first two scripts of the next season, so they were relieved to have it approved.

So, no doubt, were many of the attendees, who included “Girls” cast members like Adam Driver, Allison Williams, Jemima Kirke and Zosia Mamet. Fellow HBO-er John Oliver also made an appearance, as did Rita Wilson, who has a supporting role in “Girls.” Also spotted were comedienne Kathy Griffin, “Broad City” duo Ilana Glazer and Abbi Jacobson, plus “Saturday Night Live” cast members Cecily Strong and Kyle Mooney.

After a screening of two of this season’s episodes, the entire group made its way to a dinner held beneath the Museum’s famous suspended giant whale. Nothing there was put under glass except some mixed drinks.

(Pictured: Zosia Mamet, Lena Dunham, Allison Williams and Jemima Kirke at the “Girls” season four premiere.)

The new season of “Girls” will begin this at 9 p.m. Jan. 11 on HBO.