Radio detection of air-showers is a mature technique that has gained momentum over the past decades. With increasingly large-scale experiments, massive air-shower simulations are needed to evaluate the radio signal at each antenna position. Radio Morphing was developed for this purpose. It is a semi-analytical tool that enables a fast computation of the radio signal emitted by any air-shower at any location, from the simulation data of one single reference shower at given positions. It relies on simple electromagnetic scaling laws of the radio emission (i.e., electric field) at the antenna level and then an interpolation of the radio pulse at the desired positions. We present here major improvements on the Radio Morphing method that have been implemented recently. The upgraded version is based on revised and refined scaling laws, derived from physical principles. It also includes shower-to-shower fluctuations and a new spatial interpolation technique, thanks to which an excellent signal timing accuracy of a fraction of nanosecond can be reached. This new implementation, provides simulated signals with relative differences on the peak-to-peak amplitude of ZHAireS simulations below 10% (respectively 25%) for 91% (99%) of antennas while the computation time was reduced by more than 2 orders of magnitude compared to standard simulations. This makes Radio Morphing an efficient tool that allows for a fast and accurate computation of air-shower radio signals. Further implementation of Askaryan emission or enabling to use an input value of the geomagnetic field should reduce relative differences with ZHAireS by few percents and make the method more universal.