In this work, we propose a set of high-level canonical piecewise linear (HL
-CPWL) functions to form a representation basis for the set of piecewise li
near functions f: D bar right arrow R-1 defined over a simplicial partition
of a rectangular compact set D in R-n, In consequence, the representation
proposed uses the minimum number of parameters. The basis functions are obt
ained recursively by multiple compositions of a unique generating function
gamma, resulting in several types of nested absolute-value functions. It is
shown that the representation in a domain in R-n requires functions up to
nesting level n, As a consequence of the choice of the basis functions, an
efficient numerical method for the resolution of the parameters of the high
-level (HL) canonical representation results. Finally, an application to th
e approximation of continuous functions is shown.