The unwinding of nucleic acid secondary structures within cells is crucial to maintain genomic integrity and prevent abortive transcription and translation initiation. DHX36, also known as RHAU or G4R1, is a DEAH-box ATP-dependent helicase highly specific for DNA and RNA G-quadruplexes (G4s). A fundamental mechanistic understanding of the interaction between helicases and their G4 substrates is important to elucidate G4 biology and pave the way toward G4-targeted therapies. Here we analyze how the thermodynamic stability of G4 substrates affects binding and unwinding by DHX36. We modulated the stability of the G4 substrates by varying the sequence and the number of G-tetrads and by using small, G4-stabilizing molecules. We found an inverse correlation between the thermodynamic stability of the G4 substrates and rates of unwinding by DHX36. In stark contrast, the ATPase activity of the helicase was largely independent of substrate stability pointing toward a decoupling mechanism akin to what has been observed for many double-stranded DEAD-box RNA helicases. Our study provides the first evidence that DHX36 uses a local, non-processive mechanism to unwind G4 substrates, reminiscent of that of eukaryotic initiation factor 4A (eIF4A) on double-stranded substrates.