We present V, R photometry of the globular cluster system (GCS) of the elliptical galaxy NGC 1404 in the Fornax cluster. We derive a specific frequency of S = 2.3 +/- 0.3. The turnover of the luminosity (LF) of the GCS of NGC 1404 is at V = 24m.1 +/- 0m.2. We derive a mean colour of (V - R)mean = 0m.51. The galaxy itself is redder by about 0m.1 in (V - R) or approximately 0m.3 in (B - V). We discuss that, although NGC 1404 is at the distance of the Fornax cluster, it may not be a cluster member. This would explain the high X-ray luminosity, the low specific frequency, and the high radial velocity of this galaxy.