Here we prove that if x k , k = 1 , 2 , … , n + 2 are the zeros of ( 1 − x 2 ) T n ( x ) where T n ( x ) is the Tchebycheff polynomial of first kind of degree n , α j , β j , j = 1 , 2 , … , n + 2 and γ j , j = 1 , 2 , … , n + 1 are any real numbers there does not exist a unique polynomial Q 3 n + 3 ( x ) of degree ≤ 3 n + 3 satisfying the conditions: Q 3 n + 3 ( x j ) = α j , Q 3 n + 3 ( x j ) = β j , j = 1 , 2 , … , n + 2 and Q ‴ 3 n + 3 ( x j ) = γ j , j = 2 , 3 , … , n + 1 . Similar result is also obtained by choosing the roots of ( 1 − x 2 ) P n ( x ) as the nodes of interpolation where P n ( x ) is the Legendre polynomial of degree n .