Almonds are one of the most popular nuts, cultivated in countries with Mediterranean climates. In an almond orchard of the self-incompatible cultivar ‘Ferragnes’ in Greece, a tree with different morphological characteristics and signs of self-compatibility was observed. The aim of this study was to study the phenotype, investigate the self-compatibility trait, and elucidate the phylogenetic background of this tree, named ‘Mars’. Morphological traits and kernel and nut characteristics were measured in ‘Mars’, ‘Ferragnes’, ‘Tuono’, and ‘Lauranne’ cultivars. The self-compatibility trait of almonds is attributed to the Sf allele; thus, its existence was investigated in ‘Mars’ by PCR amplification. Moreover, the S-RNase genes of all the cultivars were sequenced. The genetic profile of ‘Mars’ was identified using eight SSR molecular markers and compared with the ‘Ferragnes’, ‘Ferraduel’, ‘Texas’, ‘Tuono’, and ‘Lauranne’ cultivars. The morphological traits suggest that ‘Mars’ is more similar to the ‘Ferragnes’ cultivar, while it bears the Sf allele. S-RNases sequencing revealed that ‘Mars’ has the genotype S1Sf, and the SSR markers showed that it is differentiated genetic material, suggesting it is a cross between ‘Ferragnes’ and ‘Tuono’. Therefore, ‘Mars’ is evaluated as a self-compatible variety with interesting agronomic traits for use in new mono-cultivar almond plantations.