Let
q
:
C
^
→
C
^
q:\hat {\mathbb C} \to \hat {\mathbb C}
be any quadratic polynomial and
r
:
C
2
∗
C
3
→
P
S
L
(
2
,
C
)
r:C_2*C_3 \to PSL(2,{\mathbb C})
be any faithful discrete representation of the free product of finite cyclic groups
C
2
C_2
and
C
3
C_3
(of orders
2
2
and
3
3
) having connected regular set. We show how the actions of
q
q
and
r
r
can be combined, using quasiconformal surgery, to construct a
2
:
2
2:2
holomorphic correspondence
z
→
w
z \to w
, defined by an algebraic relation
p
(
z
,
w
)
=
0
p(z,w)=0
.