Thin films of PbZr0.52Ti0.48O3 (PZT) with largely detached columnar grains, deposited by pulsed laser deposition (PLD) on amorphous glass substrates covered with Ca2Nb3O10 nanosheets as growth template and using LaNiO3 electrode layers, are shown to exhibit very high unipolar piezoelectric strain and ultra-low strain hysteresis. The observed increase of the piezoelectric coefficient with increasing film thickness is attributed to the reduction of clamping, because of the increasingly less dense columnar microstructure (more separation between the grains) with across the film thickness. A very large piezoelectric coefficient (490 pm/V) and a high piezoelectric strain (~0.9%) are obtained in 4-μm-thick film under an applied electric field of 200 kV/cm, which is several times larger than in usual PZT ceramics. Further very low strain hysteresis (H≈2-4%) is observed in 4 to 5 μm thick films. These belong to the best values demonstrated so far in piezoelectric films. Fatigue testing shows that the piezoelectric properties are stable up to 1010 cycles. The growth of high quality PZT films with very large strain and piezoelectric coefficients, very low hysteresis and with long-term stability on a technologically important substrate as glass is of great significance for the development of practical piezo driven microelectromechanical actuator systems.