In its classical form particles image velocimetry extracts two components of the flow velocity vector by measuring the displacement of tracer particles within a double-pulsed laser light sheet. The method described in this paper is based on the additional recording of a third exposure of the tracer particles in a parallel light sheet, which is slightly displaced with respect to the first one. The particle images resulting from these three exposures are stored on separate frames. The locations of the correlation peaks, as obtained by cross-correlation methods, are used to determine the projections of the velocity vectors onto the plane between the two light sheets. The amplitudes of these peaks are used to obtain information about the velocity component perpendicular to the light-sheet planes. The mathematical background of this method is described. Numerical simulations show the influence of the main parameters (e.g., light-sheet thickness, light-sheet displacement and out-of-plane flow component) on the resolution and reliability of the new method. A new recording procedure and its results will be shown to demonstrate the ease of operation when applying this technique to liquid flows.