Galitski's Exploring Quantum Mechanics says on its page 29,
(There are $N^2$ linearly) independent Hermitian matrices of rank $N$. The number of independent unitary matrices is also $N^2$, since there is a relation between them and Hermitian matrices $U=\text{exp}(iF).$
As I understand how to construct the Hermitian basis of $F^{n\times n}$ with 'standard basis' matrices $E_{ij}$, I understand the first half of the statement. But is the relation $U=\text{exp}(iF)$ relevant? How can I construct a unitary basis from the given Hermitian basis?