CONCORD, N.H. (AP) – Next month’s primary won’t be derailed by a state Supreme Court ruling that the way the state lists candidates on its general election ballots is unconstitutional, the court said Friday.

But the state must adopt a new way of organizing the ballots before the general election in November, the court said.

“I’m pleased that the primary ballot can remain because we’ve reached the point where people have already been voting,” said Secretary of State William Gardner, noting that absentee ballots already had be mailed out.

Last week, the high court struck down a state law that traditionally has given Republicans top billing on election ballots. The law required candidates of the party that won the previous election to be listed first for the next one.

The court ruled unanimously that the system could give an unfair advantage to the winning party. Using the same logic, the court struck down the practice of alphabetizing the names of candidates within a party who are running for the same office.

Though the court ruled in a case involving general elections, the case prompted immediate concerns for the state’s primary election, scheduled for Sept. 12. The reason is that state law governing primaries still requires alphabetizing names.

On Monday, Gardner asked the court to let the primary go forward without changing the ballot. He also asked the court to exempt this year’s general election to give the Legislature time to adopt a constitutional ballot system.

The court said Friday it had not been asked to consider the design of primary ballots, and so the ruling did not apply to them. But it rejected his request to also exempt this year’s general election, saying there was time to fix the system.

Gardner agreed, saying “We have the time to do it.”

Republicans have long dominated New Hampshire elections. The court noted that Democrats last topped the ballot in 1966, based on having the most total votes statewide in President Lyndon Johnson’s 1964 landslide.

The suit, which was filed on behalf of a group of politicians and the state Democratic Party, originally sought changes for the 2004 election, but a judge said the issues needed more analysis and debate.

Paul Twomey, the lawyer representing the group that sued, said Friday his clients were pleased the court had reaffirmed its ruling. He said the court gave the state a clear outline of what needs to change before the general election.

During trial in Superior Court, experts disagreed about the existence and strength of the so-called “primacy effect.” In defending the current system, the state also warned that changing the ballots might confuse voters.

But the judge sided with the Democrats’ expert, who said top billing helps most when voters are poorly informed, have conflicting information about a race or face lengthy or complicated choices.