The number of unemployed aged 15-74 amounted to 434 000 people in May 2010, of these 236 000 were men and 198 000 women. Compared to May 2009 the differences are not statistically significant.
"It is the first time in a year and a half that there is no increase from a yearly perspective," SCB wrote in a statement on Tuesday.
Full-time students accounted for 40 percent, or 175,000, of the figure.
Among young people aged aged 15-24, 27.8 percent or 176,000 were unemployed, out of which 64 percent, or 112 000, were full-time students.
A total of 145,000 people, around a third of total unemployment, were in long-term unemployment.
The SCB figures indicate that there remain differences between the sexes, with unemployment among men showing a slight decrease to 9.1 percent, while the trend in unemployment among women continues to climb, to 8.5 percent.
According to the seasonally adjusted data, the number of employed persons aged 15-74 amounted to 4.514 million in May 2010, representing a continuation of the trend observed during the previous months, where the increase is occurring among men. Among women the previous decline in the number of employed persons has ceased.
The data shows that the employment rate in May 2010 was 64.4 percent, which is in line with the development in April. Again the trend for men is slightly positive, while for women it is still slightly negative.
The labour market in May included 4.948 million people according to the seasonally adjusted data, showing a positive trend for both sexes.
According to the data the labour force rate (the labour force share of the population) amounted to 70.5 percent.