In many textbooks, it is written that:
The value of rate constant depends on the nature of the reactants, temperature and catalyst. It is independent of the concentration of the reactants.
However, the unit of the rate constant is
$$\left(\frac{\mathrm{mol}}{\mathrm{l}}\right)^{1-n} \mathrm{s}^{-1}$$
where $n$ is the order of reaction.
Therefore, except for first order reactions, the unit of the rate constant will have a concentration term $\displaystyle\frac{\textrm{mol}}{\textrm{l}}$ for all other reactions. Does this contradict the statement given in books?