It is proved that the Mandelbrot set associated with the pair of maps
w
1
,
2
:
C
→
C
,
w
1
(
z
)
=
s
z
+
1
,
w
2
(
z
)
=
s
∗
z
−
1
{w_{1,2}}:{\mathbf {C}} \to {\mathbf {C}}, {w_1}(z) = sz + 1, {w_2}(z) = {s^\ast }z - 1
, with parameter
s
∈
C
s \in {\mathbf {C}}
, is connected and has piecewise smooth boundary.