It is well known that the number of isolated singular points of a hypersurface of degree d in ℂP^m does not exceed the Arnol'd number A_m(d), which is defined in combinatorial terms. In the paper it is proved that if b_m-1 ^± (d) are the inertia indices of the intersection form of a nonsingular hypersurface of degree d in ℂP^m, then the inequality A_m(d) < mm{b _m-1 ⁺(d),b_m-1 ^-(d)} holds if and only if (m - 5)(d - 2) ≥ 18 and (m,d) ≠ (7, 12). The table of the Arnol'd numbers for 21 ≤ m ≤ 14, 3 ≤ d ≤ 17 and for 3 ≤ m ≤ 14, d = 18, 19 is given.