Pairwise comparisons constitute a popular and important tool for multiple-criteria decision making. Consistency is one particular aspect of pairwise comparisons that has been studied thoroughly in recent decades since human judgements are seldom fully consistent. The aim of this paper is to propose a new simple and intuitive iterative Step-by-Step (SBS) algorithm for inconsistency reduction of a (multiplicative) pairwise comparison matrix based on step-by-step changes of the most inconsistent matrix element, where the inconsistency is measured by a modified Koczkodaj's inconsistency index. A comparison of the proposed SBS algorithm with other algorithms for inconsistency reduction is provided as well.