In [20] and [22], the author proved that the union of two linear star-configurations in $mathbb{P}^2$ of type $t{ imes}s$ with $3{leq}t{leq}10$ and $t{leq}s$ has generic Hilbert function. In this paper, we prove that the union of two linear star-configurations in $mathbb{P}^2$ of type $t{ imes}s$ with $3{leq}t$ and $({aatop2})-1{leq}s$ has also generic Hilbert function.