The origin of the anomalous, 400% increase of the piezoelectric coefficient in Sc(x)Al(1-x)N alloys is revealed. Quantum mechanical calculations show that the effect is intrinsic. It comes from a strong change in the response of the internal atomic coordinates to strain and pronounced softening of C33 elastic constant. The underlying mechanism is the flattening of the energy landscape due to a competition between the parent wurtzite and the so far experimentally unknown hexagonal phases of the alloy. Our observation provides a route for the design of materials with high piezoelectric response.