We characterize the homogeneous weighted Herz space $\dot{K}^{\a ,p}_q(w_1,w_2)$ and 
the non-homogeneous weighted Herz space $K^{\a ,p}_q(w_1,w_2)$ using wavelets 
in $C^1(\R^n)$ with compact support. 
Applying the characterizations, we prove that the wavelet basis forms an unconditional 
basis in $\dot{K}^{\a ,p}_q(w_1,w_2)$ and in $K^{\a ,p}_q(w_1,w_2)$.