  We investigate the modified trace distance measure of coherence recently
introduced in [Phys. Rev. A 94, 060302(R) (2016)]. We show that for any
single-qubit state, the modified trace norm of coherence is equal to the
$l_{1}$-norm of coherence. For any $d$-dimensional quantum system, an
analytical formula of this measure for a class of maximally coherent mixed
states is provided. The trade-off relation between the coherence quantified by
the new measure and the mixedness quantified by the trace norm is also
discussed. Furthermore, we explore the relation between the modified trace
distance measure of coherence and other measures such as the $l_{1}$-norm of
coherence and the geometric measure of coherence.
