Ono conjectured that the inequality 27(b^2 + c^2 - a^2)^2 (a^2 + c^2 - b^2)^2 (a^2 + b^2 - c^2)^2<=(4K)^6 holds true for all triangles, where a, b, and c are the lengths of the sides and K is the area of the triangle. This conjecture was shown to be false by Quijano, although it was subsequently proved to be true for acute triangles by Balitrand. A simple counterexample is provided by the triangle with a = 3/4, b = 1/2, and c = 1.