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MAGIC is a system of two Imaging Atmospheric Cherenkov Telescopes located onthe Canary Island of La Palma and dedicated to the study of very high energygamma rays above 30 GeV. MAGIC has recently demonstrated its capability as aneutrino detector, by exploiting the Earth-skimming technique. Theneutrino-event selection has been studied by pointing the telescopes towardsthe sea a few degrees below the horizon, with no pre-defined source direction.An upper limit to the $\nu_\tau$ flux was set. In this work, a follow-upstrategy of given source directions is presented. This new approach ischaracterised by pointing to targets passing through the sea window observablewith MAGIC and for which a trigger from dedicated neutrino observatories isissued with large significance. Above a few tens of PeV, the acceptance ofMAGIC to $\nu_\tau$ is considerably large and compelling results can beobtained for transient events of short duration. The performance of this newmethod is tested on a sample of data collected by pointing MAGIC for a few daysfrom March to May 2016 towards the direction of a multi-PeV neutrino thatIceCube detected on June 11th 2014 (reconstructed direction (J2000.0) RA:110.34$^\circ$ and Dec.: 11.48$^\circ$). A selection cut is studied in order todiscriminate $\tau$-lepton-induced air showers from the background of veryinclined cosmic-ray-induced air showers. An upper limit on the neutrino fluxfrom the above given neutrino direction is presented.

MAGIC as a high-energy $\nu_\tau$ detector: performance study to follow-up IceCube transient events