In this paper we consider a Cartan space Cⁿ=(M,K(x,p)) with the metric K(x,p)=(a^ijkh(x)p_ip_jp_kp_h)^1/4 and a deformation using ω(x,p)=b_i(x)p_i. We call it a Randers- Quartic Cartan space and we are going to study some of its properties