We study an assembly-type bias parametrized by the dimensionless spin parameter that affects massive structures. In numerical simulations, higher spin haloes are more strongly clustered than lower spin haloes of equal mass. We detect a difference of over 30 per cent in the clustering strength for dark matter haloes of 1013–1014 h−1 M⊙, which is similar to the result of Bett et al. We explore whether the dependence of clustering strength on halo spin is removed if we apply the redefinition of overdensity peak height proposed by Lacerna & Padilla (Paper I) obtained using assembly ages. We find that this is not the case due to two reasons. First, only a few objects of low virial mass are moved into the mass range where the spin introduces an assembly-type bias after using this redefinition. Secondly, this formalism does not alter the mass of massive objects. In other words, the sample of haloes with redefined mass M in the high-mass regime is practically the same as before the redefinition of peak height, and thus the clustering behaviour is the same. We then repeat the process of finding the redefined peak height of Paper I but using the spin. In this case, the new masses show no spin-related assembly bias but they introduce a previously absent assembly bias with respect to relative age. From this result, we conclude that the assembly-type bias with respect to the halo spin has a different origin from that with respect to the assembly age. The former may be due to the material from filaments, which is accreted by massive haloes, and enhanced in high-density environments, thus causing more extreme spin values without significantly changing the formation age of the halo. In addition, the estimates of the mass of collapsed structures in numerical simulations could be lower than the true mass, even in cluster-size haloes. High-mass objects may correspond, in some cases, to a different peak height from that suggested by their virial mass, providing a possible explanation for the assembly-type bias with respect to the spin.