How do white male executives handle it when a woman or person of color become CEOs of their company? Not well, a new study from the University of Michigan's Ross School of Business suggests.

The study, which looked at more than 1,000 top executives at large and mid-sized U.S. public companies found that white male managers on average experienced a "lower sense of identity with their company" after the appointment of a female and/or racial minority CEO.

Researchers found that white male executives working under a female and/or racial minority were also less likely to provide help to fellow colleagues, with an especially negative effect on help provided to minority status colleagues.

Michigan Ross professor Jim Westphal called the responses his research team received from participants "unfortunate."

He warned that the tendency of white male executives to avoid helping female and racial minority colleagues could "harm the career prospects" of workers who are already under-represented in leadership roles.

"Our study identifies an important mechanism by which such appointments may, counterintuitively, harm the career prospects of other female and racial minority managers by reducing the amount of help that they receive from their white male colleagues," Westphal said in a statement.

He also said the lack of support shared between colleagues in the office could reflect poorly on the CEO as a result.

Women and people of color are already more likely to be promoted to high leadership levels within companies during times of crisis, a phenomenon known as the "glass cliff." If they are unable to lead their companies out of a crisis, they are quickly replaced by white men, according to a 2014 study on the phenomenon.

The study, titled "One Step Forward, Two Steps Back," is set to be published in the April issue of the Academy of Management Journal and is one of the first of its kind to systematically analyze how "important internal stakeholders" respond to the appointment of a female and/or racial minority CEO.

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As it stands, only 27, or 5.4 percent, of Fortune 500 CEOs are women. Meanwhile, only three Fortune 500 companies have black male leaders, according to Fortune.com. None of the companies are led by a black woman.

Despite that, an Ernst & Young national survey involving 1,000 full-time workers in the U.S. found that more than a third of all respondents think an increased focus on diversity in the workplace has resulted in white male candidates being overlooked.