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.