The cytogenomics-based methodology of Directional Genomic Hybridization (dGH™) emerged from the concept of strand-specific hybridization, first made possible by Chromosome Orientation FISH (CO-FISH), the utility of which was demonstrated in a variety of early applications, often involving telomeres. Similar to standard whole chromosome painting (FISH), dGH™ is capable of identifying inter-chromosomal rearrangements (translocations between chromosomes), but its distinctive strength stems from its ability to detect intra-chromosomal rearrangements (inversions within chromosomes), and to do so at higher resolution than previously possible. dGH™ brings together the strand specificity and directionality of CO-FISH with sophisticated bioinformatics-based oligonucleotide probe design to unique sequences. dGH™ serves not only as a powerful discovery tool—capable of interrogating the entire genome at the megabase level—it can also be used for high-resolution targeted detection of known inversions, a valuable attribute in both research and clinical settings. Detection of chromosomal inversions, particularly small ones, poses a formidable challenge for more traditional cytogenetic approaches, especially when they occur near the ends or telomeric regions. Here, we describe Telo-dGH™, a strand-specific scheme that utilizes dGH™ in combination with telomere CO-FISH to differentiate between terminal exchange events, specifically terminal inversions, and an altogether different form of genetic recombination that often occurs near the telomere, namely sister chromatid exchange (SCE).