  We prove that a graph has an infinitesimally rigid placement in a
non-Euclidean normed plane if and only if it contains a $(2,2)$-tight spanning
subgraph. The method uses an inductive construction based on generalised
Henneberg moves and the geometric properties of the normed plane. As a key
step, rigid placements are constructed for the complete graph $K_4$ by
considering smoothness and strict convexity properties of the unit ball.
