It’s 2015, and nearly 5% of Fortune 500 companies are still run by all-male boards of directors.

That’s the finding of a recent Fortune analysis in collaboration with S&P Capital IQ on the gender composition of Fortune 500 boards. The list is based on the latest available data in the S&P Capital database as of early January.

But here’s the encouraging news: The number of Fortune 500 companies with no female directors is down by 54% from 2013, when researchers at Catalyst had found that 50 Fortune 500 companies had all-male boards. A variety of reasons are behind the decline. Some companies on Catalyst’s 2013 list have dropped out of the Fortune 500. A few have since been acquired by companies with women on their boards. Still, others may have named a woman in response to the ever-increasing pressure to make corporate boards more diverse.

Despite this progress, several female business leaders told Fortune that it’s unacceptable for even one Fortune 500 company to be run by an all-male board.

“It is not okay for a company to have a board that does not represent the views of their customers, and women are influential decision-makers, if not the key decision-makers, in many buying decisions,” said Maureen O’Connell, the CFO at Scholastic Corp. “Also, women often have a different style for interacting with other board members. For example, women tend to bring skills such as the ability to build consensus and to be inclusive in decision-making, which can lead to be better problem solving.”

It’s important to note that 28% of Fortune 500 firms list just one female director. Still, studies have shown that it takes at least three women to enhance performance and governance and achieve effective critical mass.

Fortune reached out to every company that listed no female directors. A few companies responded with news that they recently named a woman to its board and thus were removed from our list. Of the remaining 23 companies, only two provided us with a comment on our findings.

Here are the 23 Fortune 500 companies with no female directors:

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