The number of U.S. homes in the foreclosure process and lost to foreclosure both saw double-digit year-over-year declines in December, according to a report from data aggregator CoreLogic released today.

Completed foreclosures fell 21 percent on an annual basis and 3 percent on a monthly basis in December, to 56,000. To put that in perspective, completed foreclosures averaged 21,000 per month between 2000 and 2006, according to CoreLogic.

Since the financial crisis hit in September 2008, about 4.1 million homes have been lost to foreclosure, 767,000 of them in 2012.

Foreclosure inventory — the number of homes in some stage of the foreclosure process — came in at about 1.2 million homes in December, down 19.5 percent compared to December 2011 and down 4.2 percent compared to November. Foreclosure inventory in December represented about 3 percent of all homes with a mortgage, CoreLogic said.

"The most encouraging foreclosure trend reported here is that the inventory of foreclosed properties is almost 20 percent smaller than a year ago," said Mark Fleming, chief economist for CoreLogic, in a statement.

"This big improvement indicates we are working toward resolving the backlog of the most distressed assets in the shadow inventory."

Anand Nallathambi, CoreLogic’s president and CEO said the trend should continue into 2013 and "is another positive signal that the gradual healing process in the housing market is gaining traction."

Five states accounted for nearly half of completed foreclosures nationwide in 2012: California (100,000), Florida (98,000), Michigan (74,000), Texas (57,000) and Georgia (49,000).

The five states with the lowest number of homes lost to foreclosure last year were Washington, D.C. (89), Hawaii (421), North Dakota (521), Maine (537) and West Virginia (645).

States where the courts handle the foreclosure process, known as judicial foreclosure states, dominated among the five states with the highest foreclosure inventory: Florida (10.1 percent of all mortgaged homes), New Jersey (7.0 percent), New York (5.1 percent), Nevada (4.7 percent) and Illinois (4.5 percent). Among the five, only Nevada is not a judicial foreclosure state.

The five states with the lowest foreclosure inventory were Wyoming (0.4 percent), Alaska (0.6 percent), North Dakota (0.7 percent), Nebraska (0.8 percent) and Colorado (1.0 percent), CoreLogic said.

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