MAGIC is a system of two Imaging Atmospheric Cherenkov Telescopes located on the Canary Island of La Palma and dedicated to the study of very high energy gamma rays above 30 GeV. MAGIC has recently demonstrated its capability as a neutrino detector, by exploiting the Earth-skimming technique. The neutrino-event selection has been studied by pointing the telescopes towards the 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-up strategy of given source directions is presented. This new approach is characterised by pointing to targets passing through the sea window observable with MAGIC and for which a trigger from dedicated neutrino observatories is issued with large significance. Above a few tens of PeV, the acceptance of MAGIC to $\nu_\tau$ is considerably large and compelling results can be obtained for transient events of short duration. The performance of this new method is tested on a sample of data collected by pointing MAGIC for a few days from March to May 2016 towards the direction of a multi-PeV neutrino that IceCube 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 to discriminate $\tau$-lepton-induced air showers from the background of very inclined cosmic-ray-induced air showers. An upper limit on the neutrino flux from the above given neutrino direction is presented.