  We propose an experiment intended for search for an admixture of sterile
neutrino with mass m$_s$ in the range of 1-8 keV that may be detected as
specific distortion of the electron energy spectrum during tritium decay. The
distortion is spread over large part of the spectrum so to reveal it one can
use a detector with relatively poor (near 10-15%) energy resolution. A classic
proportional counter is a simple natural choice for a tritium $\beta$-decay
detector. The method we are proposing is original in two respects. First, the
counter is produced as a whole from fully-fused quartz tube allowing to measure
current pulse directly from anode while providing high stability for a long
time. Second, a modern digital acquisition technique can be used in
measurements at ultrahigh count rate - up to 10$^6$ Hz. As a result an energy
spectrum of tritium electrons containing up to 10$^{12}$ counts may be
collected in a month of live time measurements. Due to high statistics an upper
limit down to 10$^{-3}$..10$^{-5}$ can be put on sterile neutrino mixing at 95%
CL for m$_s$ in the range of 1-8 keV, that will be 1..2 orders of magnitude
better then bounds published up to now.
