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Given the Cauchy Problem $${\partial }_{t}u(x,t)+A(t){\partial }_{x}u(x,t)=0\mathit{\hspace{1em}\hspace{1em}}u(0,x)=u_0(x)$$ Nishitani [N], by making use of a change of basis by a constant matrix, transformed the real, analytic, hyperbolic matrix into the complex matrix and showed that the given Cauchy Problem is well posed in $C^{\mathrm{\infty }}$ in a neighborhood ofzero if and only if (see also [MS]) the following condition $$h{|a^{\mathrm{♯}}|}^2\ge C{t}^2{|D^{\mathrm{♯}}|}^2$$ is satisfied, where $$D^{\mathrm{♯}}={\dot{a}}^{\mathrm{♯}}{c}^{\mathrm{♯}}-{\dot{c}}^{\mathrm{♯}}{a}^{\mathrm{♯}}\text{e}h=-detA={|a^{\mathrm{♯}}|}^2-{|c^{\mathrm{♯}}|}^2.$$ In this short note, we give a very simple condition, which is equivalent to that of Nishitani (and then a necessary and sufficient for the Well-Posedness), but...