Bacteria of the genus Staphylococcus are significant challenge for medicine, as many species are resistant to multiple antibiotics and some are even to all of the antibiotics we use. One of the approaches to developing new therapeutics to treat staphylococcal infections is the use of bacteriophages specific to these bacteria or the lytic enzymes of such bacteriophages, which are capable of hydrolyzing the cell walls of these bacteria. In this study, a new bacteriophage vB_SepP_134 (St 134) specific to Staphylococcus epidermidis was described. This podophage, with a genome of 18,275 bp, belongs to the Andhravirus genus. St 134 was able to infect various strains of 12 of the 21 tested coagulase-negative Staphylococcus species and one clinical strain from the Staphylococcus aureus complex. The genes encoding endolysin (LysSte134_1) and tail tip lysin (LysSte134_2) were identified in the St 134 genome. Both enzymes were cloned and produced in Escherichia coli cells. The endolysin LysSte134_1 demonstrated catalytic activity against peptidoglycans isolated from S. aureus, S. epidermidis, Staphylococcus haemolyticus, and Staphylococcus warneri. LysSte134_1 was active against S. aureus and S. epidermidis planktonic cells and destroyed the biofilms formed by clinical strains of S. aureus and S. epidermidis.