The 85,000-member California Nurses Association is forging an alliance with the 10,000-member National Union of Healthcare Workers to form a new union made up entirely of health sector workers.

The alliance announced Thursday renews a bitter rivalry between the nurses’ union and the powerful 2 million-member Service Employees International Union, the nation’s dominant health care union and a major force in Democratic politics.

It also points to a trend that could see unions increasingly compete against each other for a dwindling pool of new members as the ranks of organized labor continue their steady decline. Health care has been one of the few areas of growth for unions in recent years.

About half of the SEIU’s members are in the health care industry. CNA is part of the 185,000-member National Nurses United, the largest nurses’ union in the country.

A top priority for the new alliance is to lure 43,000 unionized workers at Kaiser Permanente in California away from the SEIU and into the new union, to be known as NUHW-CNA and based in Oakland. That would deprive SEIU of more than $40 million a year in membership dues.

“It increases our power and experience exponentially,” said Sal Rosselli, president of NUHW. “We will now have the resources to compete with the SEIU’s millions and millions of dollars.”

Rosselli, a former SEIU leader, founded his upstart union in 2009 after he was ousted by the larger union in a bitter power struggle. Rosselli claimed the SEIU granted too many concessions to health care corporations at the expense of union members, while SEIU leaders alleged Rosselli was simply making a power grab.

In 2010, NUHW lost an election to woo 43,000 Kaiser workers away from SEIU. But the National Labor Relations Board later ruled that the election was tainted and ordered a new vote. The do over of the nation’s largest private-sector union election since 1941 is expected to take place later this year.

SEIU spokesman Steve Trossman said he’s not surprised by the agreement because the nurses’ union has been working closely with the smaller NUHW over the past few years.

“They are pursuing a losing strategy that is bad for the labor movement that they claim they are all about,” Trossman said. “We are not in a position where we can waste precious resources on internal fights instead of using those resources to organize workers who are not already in unions.”