  It was proved in 2007 by C.Bandt and H.Rao that if a system $S = \{S_1 , ...,
S_m \}$ of contraction similarities in $R^2$ with a connected attractor $K$ has
the finite intersection property, then it satisfies OSC. We construct a
self-simiilar Jordan arc in $R^3$, defined by a system $S$ , which does not
satisfy OSC and at the same time has one-point intersection property.
