High quality a-axis oriented HgBa2CaCu2Ox superconducting thin films have been epitaxially grown on (100) LaAlO3 substrates using a modified conventional two-step method which leads to reduced interdiffusion and chemical reaction between film and substrate and to achieve high Hg-vapour pressure in a short time. We found that quenching at specific temperatures can control the preferred orientations of Hg-1212 films. The films quenched from 700 degrees C during a cooling cycle show predominantly a-axis orientation perpendicular to the film surface. The films exhibit a zero-resistance transition at temperatures > 120 K which is comparable to epitaxial c-axis oriented films. Also, we observed the Lorentz-force independent of resistive broadening in an applied magnetic field.