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We can obtain a non-symmetric class $2$ association scheme by a skew-Hadamardmatrix. We begin with a skew-Hadamard matrix of order $n$, construct askew-Hadamard matrix of order $2n$ by doubling construction, and anon-symmetric class $2$ association scheme of order $2n-1$. We will show thatthe association scheme obtained in this way never be schurian if $n$ is greaterthan or equal to $8$.

Non-symmetric class $2$ association schemes obtained by doubling of skew-Hadamard matrices are non-schurian