We performed a new membership analysis of the Χ1 Fornacis cluster based on the astrometric and photometric data of the Gaia-EDR3 catalogue. We searched for members over a field of more than 1000 deg2 and selected 164 cluster members. We confirmed most of the cluster members that have been previously identified in the literature based on Gaia-DR2 data and discovered new ones increasing the list of cluster members by about 60%. We obtained low-resolution spectroscopy of the cluster members, that we used to derive the spectral type of the stars and use our new sample of members to revisit some properties of the cluster.
A dynamical traceback reveals that the cluster was significantly closer to these young stellar groups in the past, which suggests a common origin. The spatial distribution of the stars shows that the cluster is mass segregated and that the few disc-bearing stars in our sample are mostly located in the central portions of the cluster. The empirical isochrone of the cluster that we derive from our membership analysis is consistent with the age of 30 Myr. However, the observed scatter in the HR diagram, in particular for the least massive cluster members, along with the age differences among the various models, call for a revision using other age-dating techniques. We estimate our sample of cluster members to be complete down to about 0.04 M☉ and argue that the initial mass function of the cluster (inferred from the distribution of the spectral types of the stars) shows little variation compared to other young stellar groups.