  We present the Y-formalism in the pure spinor quantization of superstring
theory in detail. Even if the $\omega-\lambda$ OPE is not completely free owing
to the presence of the projector reflecting the pure spinor constraint, it is
shown that one can construct at the quantum level a conformal field theory in
full agreement with the Berkovits' pure spinor formalism. The OPE's of the two
formalisms are the same if we define the relevant operators involving $\omega$
in a suitable manner. Moreover the Y-formalism at hand is utilized to find the
full expression of the covariant, picture raised $b$ antighost $b_B$, with a
reasonable amount of effort.
