Abstract: Due to resource constrain and load balancing problems in heterogeneous networks (HetNets), traditional best user association (UA) scheme might be unavailable. To this end, this paper focuses on the non-best UA scheme for K-tier HetNets, and proposes a novel m??-th best average biased received power (ABRP) UA scheme, of which a user is associated with the base station (BS) having the m-th strongest ABRP. For the proposed m-th ABRP UA scheme, modeling the positions of network elements in each tier as a homogeneous Poisson point process (PPP), and using stochastic geometry and order statistics, we perform the analysis of the probability that a typical user is associated with a BS that has the m-th strongest ABRP as well as the corresponding statistical description. Our mathematical analysis and numerical results show that for a given tier k, when the transmission power or density of BSs of the tier k is small relatively, the UA probability (m>1) increases with or . However, when the power or density of BS is large, the UA probability decreases. The proposed scheme can guide for the design of HetNets.