  The three-body F\"orster resonances ${\rm 3}\times nP_{3/2} \to nS_{1/2}
+(n+1)S_{1/2} +nP_{3/2}^{*} $ controlled by a dc electric field were realized
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 F\"orster resonance ${\rm
2}\times nP_{3/2} \to nS_{1/2} +(n+1)S_{1/2}, $ as well as the possibility of
their implementation only for states with values of the principal quantum
numbers $n\le 38$. In this paper we propose and analyze a three-body resonance
of a new type ${\rm 3}\times nP_{3/2} \to nS_{1/2} +(n+1)S_{1/2} +nP_{1/2} , $
which can be realized for arbitrary $n$. Its specific feature is also that the
third atom transits into a state with a different total angular moment $J=1/2$,
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 oscillation of the populations of
collective states, which is of interest for developing new schemes of
three-qubit quantum gates controlled by an electric field.
