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Electrochemical water splitting is an eco-friendly method for large-scale production of high-purity hydrogen (H2) and oxygen (O2), and hence, pioneering the design of efficient and economic bifunctional electrocatalysts is necessary. Here, hexagonal (Cu,Co)Se2 nanoflakes are fabricated to leverage the unique synergy between copper and cobalt for efficient hydrogen evolution reaction (HER) and oxygen evolution reaction (OER). As HER and OER catalysts, (Cu,Co)Se2 nanoflakes demonstrate low overpotentials of 104 and 250 mV, respectively, to reach current densities of 10 mA cm-2 in 1 m KOH solution, with respective Tafel slopes of 117.7 and 61 mV dec-1. The catalyst requires only 403 mV of overpotential to reach 1000 mA cm-2 in OER. XANES analyses reveal average oxidation states of Co as 2.6+ and 3+ post-HER and post-OER, respectively, while Cu remains predominantly in 2+ states. Presence of Cu around Co induces orbital rehybridization through linking Se bonds; establishing a cooperative participation between Co and Cu to facilitate overall charge-transfer processes, eventually enhancing catalytic activity of (Cu,Co)Se2. Further, (Cu,Co)Se2/NF-based overall-water-splitting electrolyzer offers low cell voltage (1.65V at 10 mA cm-2) and high durability even at a high current density (at eta 50) in 1 m KOH, thus demonstrating its commercial application prospects.