In this article we apply univariate and panel Lagrange Multiplier (LM) unit root tests with one and twostructural breaks proposed by Lee and Strazicich (2003, 2004) and Im et al. (2005) to examine housing prices for five different housing price indices (all housing, detached
housing, semi-detached housing, terrace housing and high-rise housing) in 14 states of Malaysia to test whether housing prices exhibit a random walk. Our main finding from the univariate LM unit root tests is that for the vast majority of states housing prices follow a stationary process about
a segmented trend. The results of the panel LM unit root tests provide overwhelming evidence that house prices are segmented trend reverting.