As women struggle to crack corporate America’s so-called glass ceiling, they may find more success in breaking the job barrier from the top down, a study said. The more women on a company’s board of directors, the more women are likely to be among that company’s senior management, according to the study by Catalyst, a nonprofit organization that researches and helps promote women in business.

Firms with 30% of women board directors in 2001 on average had 45% more women corporate officers by 2006, compared with ones with no female board members, it said on Wednesday.

Companies with the lowest percentages of women board directors in 2001 on average had 26% fewer female corporate officers than those with the highest number five years later, the study said. Those with two or more women board members in 2001 had 25% more female corporate officers by 2006 than those with just one woman board member.

“What this shows is that the number of women, or more women, more directors today, predicts pretty reliably more women in leadership five years from now,” said Ilene Lang, president of Catalyst. “There is a very strong correlation and a very strong predictor ability,” she said.

The number of Fortune 500 companies with 25% or more women on their boards is growing as well, Catalyst said. In 2001, 30 companies fit that criteria and that number grew to 68 in 2007, according to Catalyst data.

“Companies that build up the representation of women on the board and, especially if they’re at 25% today , this shows them a road map, a path, for how they can increase women in leadership tomorrow,” Lang said. Catalyst said it studied 359 companies in the Fortune 500 in 2000, 2001, 2006 and 2007.