Boolean network is a popular and well-established modelling framework for gene regulatory networks. The steady-state behaviour of Boolean networks can be described as attractors, which are hypothesised to characterise cellular phenotypes. In this work, we study the target control problem of Boolean networks, which has important applications for cellular reprogramming. More specifically, we want to reduce the total number of attractors of a Boolean network to a single target attractor. Different from existing approaches to solving control problems of Boolean networks with node perturbations, we aim to develop an approach utilising edgetic perturbations. Namely, our objective is to modify the update functions of a Boolean network such that there remains only one attractor. The design of our approach is inspired by Thomas’ first rule, and we primarily focus on the removal of cycles in the interaction graph of a Boolean network. We further use results in the literature to only remove positive cycles which are responsible for the appearance of multiple attractors. We apply our solution to a number of real-life biological networks modelled as Boolean networks, and the experimental results demonstrate its efficacy and efficiency.