Experiment QUIJOTE (Q-U-I JOint TEnerife) is a scientific collaboration, leaded by the Instituto de Astrofísica de Canarias (IAC), which can measure the polarization of the Cosmic Microwave Background (CMB) in the range of frequency up to 200 GHz, at angular scales of 1°. The project is composed of 2 telescopes and 3 instruments, located in Teide Observatory (Tenerife, Spain). After the successful delivery of the first telescope (operative since 2012), Idom is currently involved on the turn key supply of the second telescope (phase II). The work started in June 2013 and it will be completed in a challenging period of 12 months (operative at the beginning of July 2014), including design, factory assembly and testing, transport and final commissioning on site. This second unit will improve the opto-mechanical performance and maintainability. The telescope will have an unlimited rotation capacity in azimuth axis and a range of movement between 25°-95° in elevation axis. An integrated rotary joint will transmit fluid, power and signal to the rotary elements. The pointing and tracking accuracy will be significantly below to specification: 1.76 arcmin and 44 arcsec, respectively. This project completes Idoḿs contribution during phase I, which also comprises the integration and functional tests for the 5 polarimeters of the first instrument in Bilbao headquarters, and the design and supervision of the building which protects both telescopes, including the installation and commissioning of the mechanism for shutters aperture.