  The paper gives an accurate description of the qualitative structure of an
admissible BV solution to a strictly hyperbolic, piecewise genuinely nonlinear
system of conservation laws. We prove that there are a countable set $\Theta$
which contains all interaction points and a family of countably many Lipschitz
curves $\T$ such that outside $\T\cup \Theta$ $u$ is continuous, and along the
curves in $\T$, u has left and right limit except for points in $\Theta$. This
extends the corresponding structural result in \cite{BL,Liu1} for admissible
solutions.
  The proof is based on approximate wave-front tracking solutions and a proper
selection of discontinuity curves in the approximate solutions, which converge
to curves covering the discontinuities in the exact solution $u$.
