  In this work we make use of a general relativistic method to estimate the
mass-to-distance ratio M/D = 3.54^{+0.2}_{-0.2} X 10^4 M_{sun}/Mpc of the black
hole hosted at the core of the active galactic nucleus of TXS 2226-184, along
with its Right Ascension offset and the recession redshift (velocity) of the
galaxy. Our statistical fit is based on the frequency shift of photons emitted
by water masers and their orbital positions when circularly revolving around
the black hole center within the accretion disk of the active galactic nucleus.
By taking into account a previously reported distance to the galaxy, we compare
the result of the black hole mass fit to an estimate based on a mass-luminosity
correlation. We find that the black hole mass at the core of TXS 2226-184
obtained with the aid of the statistical fit using the general relativistic
method, M = 3.67 ^{+0.2}_{-0.2} X 10^6 M_{sun}, is approximately 0.6 times the
black hole mass, M_{BH} = 6.24^{+3.6}_{-2.3} X 10^6 M_{sun}, computed with the
mass-luminosity correlation.
