Abstract: In this paper, we introduce a new class of two-parametric penalized function,which includes the penalized minimum function and the penalized Fischer-Burmeister function over symmetric cone complementarity problems. We propose that this class of function is a class of complementarity functions（C-function）. Moreover, its merit function has bounded level set under a weak condition. 

Key words: complementarity problem, symmetric cone, C-functions, R01 function, boundedness, Euclidean Jordan algebra