The three-body Förster resonances 3 nP3/2(|M|) →nS1/2 + (n + 1)S1/2 + nP3/2(|M∗|), controlled by a constant electric field, were realised earlier by the authors in an ensemble of several cold Rydberg Rb atoms. One of the drawbacks of such resonances for potential application in three-qubit quantum gates is the proximity of the two-body Förster resonance 2 nP3/2 → nS1/2 + (n + 1)S1/2, as well as the possibility of their implementation only for states with values of the principal quantum numbers n 38. A three-body resonance of a new type, 3 nP3/2 → nS1/2 + (n + 1)S1/2 + nP1/2, which can be realised for arbitrary n, is proposed and analysed. Its specific feature is also that the third atom transits into a state with a different total angular momentum J = 1/2, which has no Stark structure, so that the two-body resonance is completely absent. Numerical calculations showed that for not too strong interaction, it is possible to observe coherent three-body oscillations of the populations of collective states, which is of interest for developing new schemes of three-qubit quantum gates controlled by an electric field.