Retrieving the household electricity consumption at individual appliance level is an essential requirement to assess the contribution of different end uses to the total household consumption, and thus to design energy saving policies and user-tailored feedback for reducing household electricity usage. This has led to the development of nonintrusive appliance load monitoring (NIALM), or energy disaggregation, algorithms, which aim to decompose the aggregate energy consumption data collected from a single measurement point into device-level consumption estimations. Existing NIALM algorithms are able to provide accurate estimate of the fraction of energy consumed by each appliance. Yet, in the authors' experience, they provide poor performance in reconstructing the power consumption trajectories overtime. In this brief, a new NIALM algorithm is presented, which, besides providing very accurate estimates of the aggregated consumption by appliance, also accurately characterizes the appliance power consumption profiles overtime. The proposed algorithm is based on the assumption that the unknown appliance power consumption profiles are piecewise constant overtime (as it is typical for power use patterns of household appliances) and it exploits the information on the time-of-day probability in which a specific appliance might be used. The disaggregation problem is formulated as a least-square error minimization problem, with an additional (convex) penalty term aiming at enforcing the disaggregate signals to be piecewise constant overtime. Testing on household electricity data available in the literature is reported.