It’s a start.

The San Francisco Museum of Modern Art will announce Friday, Feb. 15, the sale at auction of a major work from its collection by the artist Mark Rothko. The untitled work from 1960 is expected to bring $35 million to $50 million.

The move, said director Neal Benezra, will “enhance (the museum’s) contemporary holdings, and address art historical gaps.” Significantly, he said, it will also address the need “to broadly diversify SFMOMA’s collection.”

Coming on the heels of a January announcement that the Fine Arts Museums of San Francisco (the de Young and the Legion of Honor) will be free on Saturdays to residents of San Francisco, it is clear that change, however incremental, is afoot at the Bay Area’s largest art institutions. That follows a growing trend across the U.S. of museums finally delivering on a long-held promise to proactively embrace all cultural and economic segments of their communities.

The choice of a painting by Mark Rothko to, in effect, trade for works by underrepresented artists carries with it a certain sense of justice. Rothko was a Russian Jewish immigrant raised by his widowed mother in Portland, Ore., whose early years were much influenced by leftist thought. He rose to fame as among the most important of the Abstract Expressionist painters, widely revered for luminous paintings that many see as deeply spiritual. He took his own life in 1970, at age 66.

Paintings by Rothko are eagerly sought by collectors. The record price at auction, though for a much larger work, is $86.9 million. Sotheby’s, the house that will handle the sale of the SFMOMA work, will exhibit it in London, Taipei and Hong Kong before its New York auction in May.

In an email, Sotheby’s President Lisa Dennison expressed optimism about the sale. “The market for Rothko is truly global,” she said. “Works from this period have done extremely well at auction — the peak of the artist’s career, situated between his two most important lifetime commissions — the Seagram Murals and the Menil chapel.”

The auction house has guaranteed a minimum return to SFMOMA from the sale, regardless of the final hammer price. Neither the museum nor Sotheby’s would reveal the amount of the guarantee, but an auction professional, asking not to be identified, said it would probably not be below $35 million.

Benezra, the SFMOMA director, and Gary Garrels, senior curator of painting and sculpture, said in a joint interview that the funds generated through the Rothko sale would be used for some immediate purchases. If enough money is raised, the museum plans to devote half to create a new acquisitions endowment.

Garrels said the aim is “being more international, being more diverse, filling some historical gaps but also strengthening some of our holdings of contemporary artists.”

When the museum reopened after a $305 million construction and renovation project, largely to accommodate the 100-year loan of the Doris and Donald Fisher Collection, critics observed that the collection was heavily weighted toward works by German male artists of the 1980s. Fewer than 16 percent of the artists shown at the opening were women, and about 6 percent were artists of color.

“The Fishers have very few women in the collection,” Garrels acknowledged, “and there are some outstanding German women artists, so those probably will be a priority for us. The Fishers have, I think, two black American artists. So, again, that’s a priority.”

He also expressed strong interest in increasing the representation of Bay Area artists in the collection.

The sale of the Rothko painting raises the ante on a bet made by the Baltimore Museum of Art last year, when it announced it would sell seven works by Andy Warhol, Franz Kline, Robert Rauschenberg and other white male artists to enable the purchase of contemporary art by women and artists of color.

Asked whether such restrictions would be placed on what might be purchased by SFMOMA, Benezra said, flatly, “No.”

SFMOMA’s approach to diversity via the collection is dramatically different from the free-admission strategy. A newly released strategic plan promises to “develop meaningful relationships with … local audiences through bold gestures and the innovative use of technology to eliminate barriers to access.” But Benezra was noncommittal about easing admission fees.

“We obviously want to provide as much access as we possibly can, and yet we can’t sacrifice our revenue streams,” Benezra said. He said the museum currently plans to partner with other Yerba Buena district cultural institutions to “create a couple of free days over the course of the next year.”

The removal of a work of art from a museum’s collection — called “deaccessioning” in museum parlance, the first step before sale or other disposal — can be controversial. The two major professional associations have strict guidelines meant to protect works of art in museum collections as a public trust. Just 14 months ago, an SFMOMA spokeswoman told The Chronicle, “We do not carry our collection as an asset (in the financial statement), on the underlying assumption that we will care for it in perpetuity.”

If art can’t be sold to generate funds to fix a leaky roof or build a new wing, however, there is one significant exception to the general rule. Because it is the collection as a whole that is sacrosanct, not the individual works within it, museums can, in effect, “trade up” by selling some objects to improve overall quality. By any measure, that is what SFMOMA is doing with the sale of the Rothko.

And it is not as though the museum, which owns five other Rothko paintings, will be without a major painting by the artist. Garrels said the work being sold is “a very good painting, but it’s not of the first rank.” Comparing it to “No. 14,” also painted in 1960, most experts would agree.

“No. 14” will stay in the SFMOMA collection. At nearly 10 feet high, it is more than triple the size of the painting going to auction. With its image of a blazing orange cloud hovering above a cold, blue hardness, “No. 14” is a blood-stirring museum picture if there ever was one. “Untitled,” a solid work that suggests a solemn brick altarpiece, has not been exhibited at the museum since 2002.