A differential equation of the form
x
(
t
)
+
a
(
t
)
x
(
t
)
=
0
,
t
⩾
0
x(t) + a(t)x(t) = 0,t \geqslant 0
, is said to be in the limit circle case if all its solutions are square integrable on
[
0
,
∞
)
[0,\infty )
. It has been conjectured in [1] that all its solutions are bounded. J. Walter recently gave a counterexample. This paper gives a method of modifying any given equation in the limit circle case with bounded solutions to produce one with unbounded solutions.