For the classical Lotka-Volterra predator-prey system, new notion I-optimal curve ξ I is introduced. This curve is disposed in the phase space of the system. The curve ξ I intersects each trajectory γ c of Lotka-Volterra system at least once. The points of ξ I possess the following optimal property: if (m, M) ξ I γ c 0 , then after a ''jump'' with magnitude I to the origin of coordinates, it hits a trajectory γ c 1 and c 1 is minimal; i.e., γ c 1 is the ''nearest'' to the stable centre. The minimality concerns the rest points of initial trajectory γ c 0 , from which the ''impulsive jumps'' (subtractings) with magnitude I to (0,0) are realized. The monotonicity, continuity, and linear asymptotical behaviour of ξ I curve are proved.