After analyzing 20 years of data from 1,500 firms, researchers behind a new study have proposed a theory: Even though a company’s leadership might make an effort to have a woman on its top management team, once it has that woman, the company makes less effort — or even resists — hiring more women for that team.

The study, conducted by Wiley Global Research, used Standard & Poor’s ExecuComp, as well as data on firms from BoardEx and Institutional Shareholder Services, to analyze the gender breakdown of executives at 1,500 public companies in the U.S. from 1992 to 2011. For each firm, they looked at female representation on the top management team and in other positions throughout the company.

The researchers found that the probability that a woman would be given a position in top management was lower if a woman already held another position on the same team. According to the study, women face an “implicit quota”: When companies hire one female executive, they promptly pat themselves on the back and give up on achieving actual gender equality.  

“One might expect if you have a company that has a woman CFO or CEO, that probably means that the firm is friendlier to women and it’s more likely to hire women,” David G. Ross, co-author of the study and an associate professor at the University of Florida, told The Huffington Post. “But it almost seems like the opposite — firms are ‘one and done.’ “

Ross said the pattern could exist because companies make an effort to achieve some level of female representation on their top management teams, but once they get one woman, they turn their attention to other things.

These findings don’t mean that women should avoid working for companies that already have a female executive or feel hopeless if they already do. On the contrary, studies like this one help identify the problem so that real changes can be made. Ross told The Huffington Post that getting more women on top management teams isn’t something that will self-correct; companies need to make an active, sustained effort to ensure that men and women have equal opportunities to rise to the top.