It has been noticed that all the known binary sequences having the asymptotic merit factor $\ge 6$ are the modifications to the real primitive characters. In this paper, we give a new modification of the character sequences at length $N=p_1p_2\dots p_r$, where $p_i$'s are distinct odd primes and $r$ is finite. Based on these new modifications, for $N=p_1p_2\dots p_r$ with $p_i$'s distinct odd primes, we can construct a binary sequence of length $2N$ with asymptotic merit factor $6.0$