The author considers the Schauder canonic form for quasilinear hyperbolic systems with r-1 independent variables $x,y_{1}, \cdots,y_{r}$, with m unknown functions $z_{1},\cdots,z_{m}$ measurable coefficients and Lipschitzian data. Either the values of the unknowns are assigned on possibly distinct hyperplanes $x = a_{i}$, $0 \le a_{i} \le a$, or certain linear combinations of the unknowns are assigned on the same hyperplanes. The author states a theorem concerning the existence and uniqueness of the solutions, and their continuous dependence on the data.