Hawaii’s job market continued to tread water in November with the unemployment holding steady at 6.5 percent for the second month in a row, the state Department of Labor and Industrial Relations reported Monday.

The state’s job market appeared to be poised for a rebound when the unemployment rate declined to a 28-month low of 6 percent in May. However, the rate has crept up, reaching a one-year high of 6.5 percent in October and November on a seasonally adjusted basis.

Hawaii’s rate has been moving in the opposite direction of the national rate, which fell to 8.6 percent in November from 9 percent in October.

The rate is derived largely from a telephone survey of households. A separate survey of businesses showed that Hawaii’s economy added 500 jobs in November on a net basis. The biggest increase was in professional and business services, which added 700 jobs. The biggest decline was in the construction sector, which lost 900 jobs. In the past 12 months, Hawaii’s economy has added 4,600 jobs on a net basis.

Among the four counties, Honolulu had the lowest rate at 5.7 percent. That was up from 5.6 percent in October and 5.5 percent in November 2010.

Maui County’s rate rose to 7.7 percent in November from 7.6 percent in October. It was down from 8.2 percent a year ago.

The rate on Kauai rose to 8.8 percent in November from 8.5 percent in October and 8.7 percent in November 2010.

In Hawaii County the rate was 9.6 percent in November, up from 9.3 percent in October but down from 9.7 percent a year ago.

The county unemployment data are not adjusted for seasonal variations.