In a rare piece of good news for New Haven’s fiscal situation, the arrival of a check from Hartford wiped away last year’s budget deficit.

With an $11.2 million reimbursement for two school construction projects, Mayor John DeStefano Jr. said the city would pay down last year’s $5.5 million budget deficit and fix an accounting oddity that precedes the mayor’s 18-year tenure. The net result is a $700,000 surplus, which DeStefano told the Board of Aldermen’s finance committee Thursday would be used to boost the city’s cash reserves to pay for emergency costs such as those related to Hurricane Irene.

The check, whose timing DeStefano said was unclear due to an auditing dispute, covers the state’s share in the 2006 construction of John C. Daniels School in the Hill and the 2000 construction of the Conte/West Hills School in Wooster Square. While it is purely a one-time revenue, the reimbursement represents a positive step in a continually improving budget outlook for the city, DeStefano said.

“I don’t want to sound too rosy about it, but the city’s finances are stabilizing,” he said.

Still, the city’s current financial picture is far from certain. A $4.3 million in the current fiscal year’s budget relies on savings on labor costs that have not yet been achieved, and several revenue sources that DeStefano had included in the budget have fallen through, such as a proposed storm water authority that aldermen rejected in the spring.

While the money needed to balance last year’s budget was only about half the amount the city received in August, DeStefano decided to use most of the leftover cash to fix an irregularity that has haunted his budget staff since the day he took office.

In a strange accounting mystery that budget supervisor Joe Clerkin said he could not explain, the city began an annual habit of booking grants from the state’s Payment in Lieu of Taxes (PILOT) program to the previous fiscal year. Because it created a one-year delay in the city’s revenue stream, the irregularity troubled the city’s auditors and rating agencies, but city spokesman Adam Joseph said it became an accepted practice over time.

DeStefano brought the city’s accounting up to date, he said, by using a portion of the state’s check to plug a hole in last year’s budget reserved for the PILOT money, which comes to the city every October. The move will help the city make a strong case to rating agencies about its fiscal position.

“This is not a new revenue stream, and it doesn’t change economic realities, but being current on everything we’re doing is important because it strengthens our cash position,” Joseph said.

While members of the finance committee praised DeStefano’s decision to use the city’s newfound surplus to replenish its reserves, Ward 5 Alderman Jorge Perez expressed displeasure that the irregularity in booking PILOT payments was in place for as long as it was. Perez said auditors should not have turned a blind eye to the practice.

“We should bring in the auditors and question them about what else we’re not hearing about,” he said.

DeStefano apologized for not bringing the city’s comptroller, Mark Pietrosimone, to the finance committee meeting to explain the irregularity’s persistence.

The city’s reserves, also known as the “rainy day” fund, stood at $16.1 million before the reimbursement check arrived. With the check, $5.5 million that would have been used to plug last year’s deficit was able to remain untouched. The $700,000 net surplus left after correcting the city’s booking error grew the reserves to nearly $17 million.

The city has not yet received a final estimate of the portion of Irene-related costs the federal government will bear, DeStefano said.