In 2008 the blazar Markarian 421 entered a very active phase and was one of the brightest sources in the sky at TeV energies , showing frequent flaring episodes .
Using the data of ARGO-YBJ , a full coverage air shower detector located at Yangbajing ( 4300 m a.s.l. , Tibet , China ) , we monitored the source at gamma ray energies E > 0.3 TeV during the whole year .
The observed flux was variable , with the strongest flares in March and June , in correlation with X-ray enhanced activity .
While during specific episodes the TeV flux could be several times larger than the Crab Nebula one , the average emission from day 41 to 180 was almost twice the Crab level , with an integral flux of ( 3.6 \pm 0.6 ) \times 10 ^ { -11 } photons cm ^ { -2 } s ^ { -1 } for energies E > 1 TeV , and decreased afterwards .

This paper concentrates on the flares occurred in the first half of June .
This period has been deeply studied from optical to 100 MeV gamma rays , and partially up to TeV energies , since the moonlight hampered the Cherenkov telescope observations during the most intense part of the emission .
Our data complete these observations , with the detection of a signal with a statistical significance of 3.8 standard deviations on June 11-13 , corresponding to a gamma ray flux about 6 times larger than the Crab one above 1 TeV .

The reconstructed differential spectrum , corrected for the intergalactic absorption , can be represented by a power law with an index \alpha = -2.1 ^ { +0.7 } _ { -0.5 } extending up to several TeV .
The spectrum slope is fully consistent with previous observations reporting a correlation between the flux and the spectral index , suggesting that this property is maintained in different epochs and characterizes the source emission processes .