The BL Lac type object 1ES 2344+51.4 (redshift $z=0.044$) was one of the first sources to be included in the extreme high-peaked BL Lac (EHBL) family. EHBLs are characterised by a broadband spectral energy distribution (SED) featuring the synchrotron peak above $\sim 10^{17}$ Hz. From previous studies of 1ES 2344+51.4 in the very-high-energy (VHE, $>$100 GeV) gamma-ray range, its inverse Compton (IC) peak is expected around 200 GeV. 1ES2344+51.4 was first detected in the VHE range by Whipple in 1995 during a very bright outburst showing around 60% of the flux of the Crab Nebula above 350 GeV. In 1996, during another flare in the X-ray band, observations with Beppo-SAX revealed a large 0.1-10 keV flux variability on timescales of a few hours and an impressive frequency shift of the synchrotron peak to above $10^{18}$ Hz. Later on, this extreme behaviour of the source motivated several multiwavelength campaigns, during most of which the source appeared to be in a low state and showing no clear signs of ``extremeness''. In August 2016, FACT detected 1ES 2344+51.4 in a high state and triggered multiwavelength observations. The VHE observations show a flux level similar to the historical maximum of 1995. The combination of MAGIC, FACT, and Fermi-LAT spectra provides an unprecedented characterisation of the IC peak. It is the first time that simultaneous HE and VHE data are presented for this object during a flaring episode. We find an atypically hard spectrum in the VHE $\gamma$-rays as well as a hard X-ray spectrum, revealing a renewed extreme behaviour.