In this paper, we use Borcherds lifting and the big CM value formula of Bruinier, Kudla, and Yang to give an explicit factorization formula for the norm of
Ψ
(
d
1
+
d
1
2
)
−
Ψ
(
d
2
+
d
2
2
)
\Psi (\frac {d_1+\sqrt {d_1}}2) -\Psi (\frac {d_2+\sqrt {d_2}}2)
, where
Ψ
\Psi
is the
j
j
-invariant or the Weber invariant
ω
2
\omega _2
. The
j
j
-invariant case gives another proof of the well-known Gross-Zagier factorization formula of singular moduli, while the Weber invariant case gives a proof of the Yui-Zagier conjecture for
ω
2
\omega _2
. The method used here could be extended to deal with other modular functions on a genus zero modular curve.