A graph of order \(\geq 3\) whose vertices (called joints) are points in \(\mathbb{R}^n\) and whose edges (called bars) are line segments connecting two vertices has been considered as a framework in \(\mathbb{R}^n\). The planar, triangle-free unit-bar-framework given by the first author in 1991 was rigid, but not infinitesimally rigid; see Discrete Appl. Math. 31, No. 2, 193-200 (1991; Zbl 0762.05045). In this paper, the authors present a unit-bar-framework in 3-space which is infinitesimally rigid and triangle-free.