This paper introduces a novel alignment-free sequence analysis methodology. Its main idea is based on introducing a new representation of the DNA-Sequence. This representation breaks the dependency between the DNA bases that exist in the traditional string presentation. We called it the Four-Lists-Representation (FLR). Based on the FLR, a series of revolutionary algorithms for searching, map-discovery, similarity-score analysis, and similarity-visualization have been developed. They are combined in what we call the FLR Methodology. The paper also studies most of the available similarity analysis techniques in a comprehensive state-of-art review. The conducted extensive simulation and theoretical studies confirm the outperformance of the whole set of FLR-based algorithms in terms of speed and memory consumption in comparison to a long list of available similarity analysis algorithms. The ability to provide a similarity-map, similarity-score, and similarity-graph as a set of evidence-based rationales makes the quality of results provided by the proposed methodology presents a new edge in this field and promises a new area of genome-based research.