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complement

SYNTAX: YP in [H' H YP], where H is a head and H' the projection of H. According to X-bar theory, the complement of a head X0 is defined either as a position attached or adjoined to X', or as a sister of X0. Thus, in configuration (i), either A and B are complements of X0, or just B (the sister of X0). 

(i)	 	X'
	       /|
	      /	|     
	     A	X'
	       /|
	      /	|
	     B	X0
Sometimes, the complement of a head X0 is equated with its internal argument(s).
LIT. Chomsky, N. (1986a)
Chomsky, N. (1981)
Williams, E. (1980)