  The strong correlation between the mass of the central supermassive black
hole (SMBH) and the bulge in some galaxies and quasars implies that the
formation of the black hole is somehow linked to the bulge. The measurement of
metallicity by NV/CIV or NV/HeII in quasars allows to discuss a possible way of
formation of the black hole. In this Letter we trace the metallicity along the
possible routes in Rees' diagram in order to test the ways by which SMBHs can
form. We derive a relation between the metallicity and the mass of the SMBH as
$Z\propto M_{BH}$ based on the numerical simulation of the evolution of star
clusters. It is in good agreement with the relation determined by the
metallicity measured by NV/CIV or NV/HeII in Hamann & Ferland's sample. This
lends observational support to the formation of SMBHs via routes R4 or R5,
namely, the evolution of dense star clusters.
