Hawaii’s unemployment rate fell for the third month in a row and hit a six-year-low of 4.1 percent in October to provide further evidence that the state economy is improving.

It was the lowest level for the seasonally adjusted jobless rate since the early stages of the recession in July 2008, when it also was 4.1 percent.

However, Hawaii employers added 2,000 fewer nonfarm payroll jobs in October from the previous month, according to data released Thursday by the state Department of Labor and Industrial Relations. The drop in payroll jobs came despite the number of people employed in the labor force rising by 2,150 to 640,150.

“When employment increases and payroll jobs decrease, that’s an indication that there are more people self-employed, said Eugene Tian, chief economist for the state Department of Business, Economic Development & Tourism.

The state’s labor force, which includes those who are employed and others who are unemployed but actively seeking work, rose to a record 667,750.

Hawaii’s recent peak for unemployment was 7.1 percent in both July and August 2009 following the recession. The all-time low was 2.3 percent in October, November and December 2006. The state unemployment rate was stuck at 4.4 percent from April through July before dipping to 4.3 percent in August and then 4.2 percent in September.