This brought the fall in house prices during 1994 down to 0.2 per cent. The annual fall in house prices had been standing at 1 per cent in November.
Gary Marsh, a spokesman for the society, said he expected the housing market to remain flat. but predicted it would pick up later in the year in line with the recovery in the British economy.
Nationwide Building Society, which uses a smaller sample for its house price survey and does not seasonally adjust the figures, reported a rise of 1.8 per cent in prices in December and an annual rise of 0.3 per cent.
Rob Thomas, housing analyst at stockbrokers UBS, is more optimistic than most, and believes house prices will end the year 6 per cent higher.Like Halifax, he believes the normal flurry of activity in the spring will not herald a revival in the market because of higher mortgage rates, a reduction in social security support for mortgage payments and a further restriction in mortgage tax relief.
But the improving economy should lead to more full time jobs, higher real incomes and an increase in house prices, he said.
New house prices fell in December by 0.1 per cent, but are 1.7 per cent higher than at the beginning of the year - mainly due to a sharp fall last December. The average price paid for a new house is £67,866 compared with £61,776 paid for all houses.First-time buyers' prices fell by 0.3 per cent in December, but are 0.1 per cent higher than a year ago.
The average price paid by a first-time buyer is £45,358.