The r-th order nonlinearity of Boolean functions is an important cryptographic criterion associated with some attacks on stream and block ciphers. It is also very useful in coding theory, since it is related to the covering radii of Reed-Muller codes. In this paper we investigate the lower bound of the higher-order nonlinearity of Niho Boolean functions f(x) = tr(λx d ) over F 2 n , where $\lambda \isin F_2_n^*$, $d = 2^{(n-1)/2} + 2^{(n-1)/4} - 1$ when n = 1 mod 4 or $d = 2^{(n-1)/2} + 2^{(3n-1)/4} - 1$ when n = 3 mod 4.

In this paper we correct the wrong proof of Lemma 7 of the above titled paper (ibid., vol. 52, no. 2, pp. 738-743, Feb. 06), which is very important to the proof of Theorem 8 of the same paper.