In this paper, the boundedness from below of multiplication operators between 
$\alpha$-Bloch spaces 
${{B}^{\alpha }},\,\alpha \,>\,0$, on the unit disk 
$D$ is studied completely. For a bounded multiplication operator 
${{M}_{u}}\,:\,{{B}^{\alpha }}\,\to \,{{B}^{\beta }}$, defined by 
${{M}_{u}}f\,=\,uf$ for 
$f\,\in \,{{B}^{\alpha }}$, we prove the following result:
(i) If 
$0<\beta <\alpha ,\,\text{or}\,\text{0}<\alpha \le \text{1}\,\text{and}\,\alpha <\beta \text{,}\,{{M}_{u}}$ is not bounded below;
(ii) if 
$0\,<\,\alpha \,=\,\beta \,\le \,1,\,{{M}_{u}}$ is bounded below if and only if lim 
${{\inf }_{z\to \partial D}}\,\left| u\left( z \right) \right|\,>\,0;$
(iii) if 
$1\,<\,\alpha \,\le \,\beta ,\,{{M}_{u}}$ is bounded below if and only if there exist a 
$\delta \,>\,0$ and a positive 
$r\,<\,1$ such that for every point 
$z\,\in \,D$ there is a point 
${{z}^{'}}\,\in \,D$ with the property 
$d\left( {{z}^{'}},\,z \right)\,<\,r$ and 
${{\left( 1\,-\,{{\left| {{z}^{'}} \right|}^{2}} \right)}^{\beta -\alpha }}\left| u\left( {{z}^{'}} \right) \right|\,\ge \,\delta$, where 
$d\left( \cdot ,\,\cdot \right)$ denotes the pseudo-distance on 
$D$.
