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Research firm CoreLogic Inc. (NYSE: CLGX) reported today that both the number and total value of residential properties with negative equity declined in the fourth quarter of the 2012. As a percentage of all properties with a mortgage, the negative equity rate fell from 22% (10.6 million properties) in the third quarter of 2012 to 21.5% (10.4 million properties). Nationally, the amount of negative equity decreased from $670 billion in the third quarter to $628 billion in the fourth quarter.

CoreLogic’s chief economist had this to say:

The scourge of negative equity continues to recede across the country. There is certainly more to do but with fewer borrowers underwater, the fundamentals underpinning the housing market will continue to strengthen. The trend toward more homeowners moving back into positive equity territory should continue in 2013.

Underwater mortgage percentages vary widely, with Nevada posting the highest reading at 52.4% and North Dakota the lowest at 5.6%. Rounding out the five states with the highest percentage of underwater mortgages are Florida (40.2%), Arizona (34.9%), Georgia (33.8%) and Michigan (31.9%). These five states combine for 32.7% of all negative equity in the United States.

In addition to North Dakota, the other four states with the lowest percentage of underwater mortgages are Montana, Maine, New York and Alaska.

CoreLogic noted that more expensive homes are faring better in terms of positive equity. Of homes valued at more than $200,000, some 82% have positive equity, compared with 72% of homes valued at less than $200,000.

Despite the improvement, CoreLogic notes that 2.3 million residential properties had less than 5% equity at the end of the fourth quarter. In the second quarter of 2012, some 1.8 million properties had less than 5% equity.

Many of these so-called “near negative equity” homes are located in states where underwater homes are relatively scarce. Colorado’s percentage of underwater homes is 17.4%, but it leads in near-negative equity homes with 6.6%. North Carolina, with just 14.1% of homes underwater has 6.4% of homes with 5% or less equity. The increase in home values with near negative equity could indicate that homes in these states are pulling themselves above water at an increasing rate, which would be another good sign for home values.

CoreLogic’s full report is available here.