  The First \fermi-LAT Catalog of Sources Above 10 GeV reported evidence of
pulsed emission above 25 GeV from 12 pulsars, including the Vela pulsar, which
showed evidence of pulsation at $>37$ GeV energy bands. Using 62 months of
\fermi-LAT data, we analyzed the gamma-ray emission from the Vela pulsar and
searched for pulsed emission above 50 GeV. Having confirmed the significance of
the pulsation in 30-50 GeV with the H-test (p-value $\sim10^{-77}$), we
extracted its pulse profile using the Bayesian block algorithm and compared it
with the distribution of the 5 observed photons above 50 GeV using the
likelihood ratio test. Pulsation was significantly detected for photons above
50 GeV with p-value $=3\times10^{-5}$ ($4.2\sigma$). The detection of pulsation
is significant above $4\sigma$ at $>79$ GeV and above $3\sigma$ at $>90$ GeV
energy bands, making this the highest energy pulsation significantly detected
by the LAT. We explore non-stationary outer gap scenario of the very
high-energy emissions from the Vela pulsar.
