  In this paper, we prove the coincidence of Kaletha's recent construction of
the local Langlands correspondence for regular supercuspidal representations
with Harris--Taylor's one in the case of general linear groups. The keys are
Bushnell--Henniart's essentially tame local Langlands correspondence and Tam's
result on Bushnell--Henniart's rectifiers. By combining them, our problem is
reduced to an elementary root-theoretic computation on the difference between
Kaletha's and Tam's $\chi$-data.
