Cells move directionally along gradients of substrate stiffness - a process called durotaxis. In the situations studied so far, durotaxis relies on cell-substrate focal adhesions to sense stiffness and transmit forces that drive directed motion. However, whether and how durotaxis can take place in the absence of focal adhesions remains unclear. Here, we show that confined cells can perform durotaxis despite lacking focal adhesions. This durotactic migration depends on an asymmetric myosin distribution and actomyosin retrograde flow. We propose that the mechanism of this focal adhesion-independent durotaxis is that stiffer substrates offer higher friction. We put forward a physical model that predicts that non-adherent cells polarise and migrate towards regions of higher friction - a process that we call frictiotaxis. We demonstrate frictiotaxis in experiments by showing that cells migrate up a friction gradient even when stiffness is uniform. Our results broaden the potential of durotaxis to guide any cell that contacts a substrate, and they reveal a mode of directed migration based on friction. These findings have implications for cell migration during development, immune response and cancer progression, which usually takes place in confined environments that favour adhesion-independent amoeboid migration.