The price of the average UK house fell by 0.1% in December with the typical UK home now worth £162,262, according to figures from Nationwide.
This is the 10th month in a row UK house prices have fallen.
Overall, prices fell by 1% last year, cancelling out the 1% rise seen in 2011, says Nationwide.
Experts say the relative calm could be seen as a resilient performance by the housing market, but warned that the outlook remains uncertain.
Robert Gardner, chief economist at Nationwide, says: "The fact that prices declined even though employment rose strongly suggests that conditions remain fragile, especially since other signs of housing market activity, such as the number of mortgage approvals, remained subdued, well below their long run averages."
The Nationwide figures show 11 of the 13 UK housing regions saw annual price falls during 2012 with London the best performing region.
"With the exception of prime properties, the North/South divide is as pronounced as ever," said Jonathan Hopper, managing director of the property search consultants, Garrington.
"In 2013, there's every reason to believe prices of mainstream properties will continue to fall in the North and rise in the South, where the economy is much more stable."