Definition
In contrast to features of a configurational language, non-configurational languages are typically characterized by a flat language structure which allows for freer word ordering and sentence construction. Similarly, arguments and adjuncts in a non-configurational language would be structurally parallel (Davis, 1993, p. 53).
This term originated as a result of languages that did not adhere to and were unaccounted for under Noam Chomsky’s universal grammar. However, most languages at some level of analysis have some features of configurationality (Davis, 1993, p. 53).
Therefore, syntactic structures for Halkomelem, Skwxwu7mesh and many other Indigenous languages continue to be investigated and determined outside of inapplicable constraints.
Examples

References
Davis, H. (1993). A configurational pronominal argument language. Proceedings of WECOL, 6, 53-67.