  We introduce a procedure to generate supersinglets, the multipartite
generalization of angular momentum singlet states. A supersinglet is defined as
a total spin zero state consisting of $ N $ spin-$ j $ particles. They are
highly entangled and have zero spin variance in any direction, and as such are
potentially useful for quantum metrology. Our scheme is based on projective
measurements that measure the collective spin of the whole spin ensemble. A
local unitary rotation is applied conditionally on the measurement outcome,
such as to maximize the probability of obtaining spin zero on the subsequent
measurement. The sequence is repeated in the $ z $- and $ x $-basis until
convergence is obtained towards the supersinglet state. Our sequence works
regardless of the initial state, and no postselection is required. Due to the
use of strong projective measurements, very fast convergence towards zero spin
variance is obtained. We discuss an example implementation using quantum
nondemolition measurements in atomic ensembles, and perform numerical
simulations to demonstrate the procedure.
