A result in balanced incomplete block designs

AbstractHall and Connor proved that non-existence of a symmetric BIBD with parameters (v, k, λ) implies non-existence of a BIBD with parameters (v′, b′, k′, r′, λ′)=(v−k, v−1, k−λ, k, λ) if λ=1 or 2. Examples are given for which the preceding is false if the condition on λ is dropped