The goal of this paper is to design sequences consist of −1 and 1 satisfying the following three conditions for a training sequence in wireless communications: the number of negatives and that of positives are balanced, and the sign of the entries in the sequence changes as often as possible, and the structure of the inverse of the Toeplitz matrix of a sequence is simple. The wireless communication channel can be estimated by multiplying the inverse of Toeplitz matrix of a training sequence and the received signal vector. The simple inverse of the Toeplitz sign matrix gives low complexity for the channel estimation by the inverse method. In this paper, we propose an alternating sign sequences of length 2n − 1 which satisfy the above properties and provide very simple inverse of their Toeplitz matrices. With the proposed sequences, we estimate the channel extremely fast by using the inverse method.