As part of a detailed study of the gas content in a sample of Early-Type galaxies , we present 21 cm H i line maps of the S0 galaxy NGC 404 , at a spatial resolution of 15.2 ^ { \prime \prime } \times 14.4 ^ { \prime \prime } ( \alpha \times \delta ) and a velocity resolution of 2.6 km s ^ { -1 } .
The H i has been traced out to a radius R \sim 8 R _ { 25 } or 48 disc scale-lengths , making it one of the largest H i extents reported ( 800 ^ { \prime \prime } or 12.6 kpc at the assumed distance of 3.3 Mpc ) .
Approximately 75 % of the H i resides in a doughnut which is seen close to face–on with inner and outer radii of \sim R _ { 25 } and \sim 4 R _ { 25 } .
The optical galaxy fits snugly within the hole of the doughnut .
The remaining 25 % of the neutral gas is found in an annulus concentric with the doughnut and with a somewhat larger ellipticity , extending from a radius of \sim 4 R _ { 25 } to \sim 8 R _ { 25 } .
A total H i mass of 1.52 \pm 0.04 \times 10 ^ { 8 } M _ { \odot } is found , which implies an M _ { H { \mbox { \scriptsize \sc i } } } / L _ { B } = 0.22 in solar units .
We argue that most if not all of this gas is of external origin , most likely due to the merger of a dwarf irregular galaxy with M _ { B } \sim - 15.5 mag .

The velocity field shows a steeply declining observed rotation curve , compatible with Keplerian decline .
However , because the galaxy is close to face–on there is a degeneracy in the determination of the intrinsic rotation curve and inclination .
We therefore analysed two extreme cases , producing tilted–ring model fits forcing either a Keplerian or a Flat rotation curve through the observations ; both approaches result in equally plausible fits .
In both model fits , the position angle of the kinematical major axis of the annulus is distinct from that of the doughnut and ranges from 160 ^ { \circ } to 120 ^ { \circ } ( for the doughnut these values are 100 ^ { \circ } to 60 ^ { \circ } ) .

Assuming a distance of 3.3 Mpc , a total mass of 3 \times 10 ^ { 10 } M _ { \odot } 
is found on the basis of the Keplerian rotation curve .
This implies a global M _ { T } / L _ { B } ratio of \sim 44 in solar units which is high and likely a reflection of the low blue luminosity of the galaxy ( \sim 15 times lower than the average S0 luminosity ) .
Values for a Flat rotation curve are a factor of 4 higher .