A flooring system employing an improved overlap system for floating installation of flooring panels. Each floor panel having a floor panel body, L-shaped panel sections and L-shaped panel receiving sections. The floor panel body is a multilayered composite structure having a bottom layer. The L-shaped panel sections are prepared on adjacent sides of the floor panel body and include a base section, a vertical support and a cut out section which is formed between the vertical support and the floor panel body. The L-shaped panel receiving sections are prepared on opposite sides of the L-shaped panel sections. The bottom layer of the floor panel has a thickness that is equal to or greater than a height of the L-shaped panel sections and depth of the L-shaped panel receiving sections. Each L-shaped panel receiving section includes a downward facing protrusion and a vertical support receiving passageway, which may engage a cut out section and receive a vertical support from another floor panel respectively. An adhesive is also applied to inner surfaces of the cut out section and vertical support receiving passageway.