In this paper, we propose BLAST, a novel backdoor attack technique for cooperative multi-agent deep reinforcement learning (c-MADRL) systems. To overcome the Limitations (lack of stealth of immediate trigger pattern, backdoor learning/activation via additional networks, and backdooring of all agents) of existing backdoor attacks, BLAST attacks the entire multi-agent team by inserting a backdoor only into a single agent. Stealth is achieved by using adversarial spatiotemporal behavior patterns as backdoor triggers, and the reward function of the backdoor agent is unilaterally induced to achieve the 'leverage attack effect'. Through experiments on VDN, QMIX, MAPPO algorithms and existing defense mechanisms in SMAC and Pursuit environments, we confirm the high attack success rate and low normal performance variance of BLAST.