By Alejandro LazoJanuary 20, 2012, 10:49 a.m.

Home sales rose nationally in December, marking the third consecutive month that the market has shown improvement.

Previously owned homes were sold at a seasonally adjusted annual rate of 4.61 million units, up 5.0% from November and 3.6% from December a year prior, according to the National Assn. of Realtors.

“The market for single-family homes picked up in the second half of 2011, after being stuck near the bottom for nearly three years,” Patrick Newport, an economist with IHS Global Insight, wrote in a note. “This pickup is real, but the road to recovery will be a slow one.”

About one in three homes sold last month was a so-called distressed sale, either a foreclosure or a short sale, the latter involving a bank allowing a home to be sold for less than the outstanding debt on the property. Roughly one in three homes was purchased in cash.

The nation’s housing inventory dropped 9.2% from the prior month, to 2.38 million homes available for sale. That represents a supply of six months and a little less than a week. Economists consider about six months of supply to be a stable market.