The main target this paper is to check a theory about dark matter nature, which was published by the author in previous papers. It was postulated and supported, with several experimental evidences, that dark matter density is a function which depend on E, gravitational field. That paper studied six big galaxies whose velocity in flat area of rotation curve is bigger than 200 km/s. Current paper studies a similar law for M33, which is an intermediate satellite galaxy of M31, it is 850 kpc away from Earth and its velocity in flat area of rotation curve is approximately 120 km/s. In this work has been calculated a new function for DM density for M33. Reader could think, why disturb me with a new DM density profile, called Bernoulli profile in this paper, whose values have relative differences with Burket ones below 2%? The reason is clear. This DM profile has been got starting from hypothesis that DM is generated by the own gravitational field. Therefore if DM Bernoulli profile fits perfectly to Burket DM profile then it is possible conclude that observational data supports author´s hypothesis about DM nature. To find reasons that author has to do so daring statement, reader can consult [1] Abarca,M.2014. Dark matter model by quantum vacuum. [2] Abarca,M.2015. Dark matter density function depending on gravitational field as Universal law. [3] Abarca,M.2015. A new dark matter density profile for NGC 3198 galaxy to demonstrate that dark matter is generated by gravitational field. Briefly will be explained method followed to develop this paper. Firstly are presented rotation curve and table with data about DM density inside halo of M33 galaxy. These data come from [4] E. Corbelli, 2014. In fourth epigraph, considering rotation curve of M33 from Corbelli data, it is right to calculate gravitational field E, through Virial theorem. So in this epigraph has been tabulate gravitational field inside a wide region of halo, from 8 kpc to 22 Kpc. In fifth epigraphs has been tabulated and plotted data of Burket DM density profile published by [4] E. Corbelli, 2014. for M33. In sixth epigraph has been fitted data of Burket DM density profile as power of gravitational field, E, with a correlation coefficient bigger than 0,999. Particularly formula found is Density of D.M = A•E^B. Where A= 29,02219371 and B= 2,242193511 into I.S. of units. In seventh epigraph it has been compared DM density as power of E and Burket profiles. Tables and plots show clearly that relative differences between both profiles are mainly below 5%. In eight epigraph it is considered derivative of gravitational field in halo region where density of baryonic matter is negligible regarding DM density. As consequence M´(r)= 4Pi•r^2•D.M Density. Considering that Density D.M = A•E^B then M´(r) = 4Pi • r^2 •A•E^B. If M´(r) is replaced on derivative of E (r) then it is got a Bernoulli differential equation whose solution allows to get a new DM density profile through formula Density D.M = A•E^B. In nineth epigraph Bernoulli and Burket DM density profiles have been compared. Its relative differences are below 2% for radius bigger than 10 kpc, which is a superb result. The tenth chapter makes a comparison between DM densities as power of E for M33 and NGC 3198 galaxies. The goal is to show a general law for galaxies: the more massive galaxy is the less DM density at a specific value of E. In the eleven chapter it is fitted DM density as power of E for a reduced data set, and it is studied its behaviour outside dominion regression. In chapter twelve DM Bernoulli profile is extrapolated up to 70 kpc and it is compared with Burket profile.