Abstract: Let SPOn be the semigroup of all strictly partial order-preserving singular transformations on a finite-chain n if n≥3,and let N(n,r)=α∈SPOn:|Imα|≤r be the two-sided ideal of the semigroup SPOn if for an arbitrary integer r such that 0≤r≤n-2.By analyzing the non-group elements and Green’s relations,the minimal non-group elements generating set,non-group rank and non-idempotent rank of the semigroup N(n,r) are obtained,respectively.Furthermore,the relative rank of the semigroup N(n,r) with respect to itself each ideal N(n,l) is determined if 0≤l≤r.