  Aims: We used 12,530 photometrically-selected blue horizontal branch (BHB)
stars from the Sloan Digital Sky Survey (SDSS) to estimate the total extinction
of the Milky Way at the high Galactic latitudes, $R_V$ and $A_V$ in each line
of sight. Methods: A Bayesian method was developed to estimate the reddening
values in the given lines of sight. Based on the most likely values of
reddening in multiple colors, we were able to derive the values of $R_V$ and
$A_V$.
  Results: We selected 94 zero-reddened BHB stars from seven globular clusters
as the template. The reddening in the four SDSS colors for the northern
Galactic cap were estimated by comparing the field BHB stars with the template
stars. The accuracy of this estimation is around 0.01\,mag for most lines of
sight. We also obtained $<R_V>$ to be around 2.40$\pm1.05$ and $A_V$ map within
an uncertainty of 0.1\,mag. The results, including reddening values in the four
SDSS colors, $A_V$, and $R_V$ in each line of sight, are released on line. In
this work, we employ an up-to-date parallel technique on GPU card to overcome
time-consuming computations. We plan to release online the C++ CUDA code used
for this analysis.
  Conclusions: The extinction map derived from BHB stars is highly consistent
with that from Schlegel, Finkbeiner & Davis(1998). The derived $R_V$ is around
2.40$\pm1.05$. The contamination probably makes the $R_V$ be larger.
