  We develop a construction of the unitary type anti-involution for the
quantized differential calculus over $GL_q(n)$ in the case $|q|=1$. To this
end, we consider a joint associative algebra of quantized functions,
differential forms and Lie derivatives over $GL_q(n)/SL_q(n)$, which is
bicovariant with respect to $GL_q(n)/SL_q(n)$ coactions. We define a specific
non-central {\em spectral extension} of this algebra by the spectral variables
of three matrices of the algebra generators. In the spectrally expended algebra
we construct three-parametric family of its inner automorphisms. These
automorphisms are used for construction of the unitary anti-involution for the
(spectrally extended) calculus over $GL_q(n)$.
