In　this　work,　a　multiple　speech　source　separation　method　using　inter-channel　correlation　and　relaxed　sparsity　is　proposed.　A　B-format　microphone　with　four　spatially　located　channels　is　adopted　due　to　the　size　of　the　microphone　array　to　preserve　the　spatial　parameter　integrity　of　the　original　signal.　Specifically,　we　firstly　measure　the　proportion　of　overlapped　components　among　multiple　sources　and　find　that　there　exist　many　overlapped　time-frequency　(TF)　components　with　increasing　source　number.　Then,　considering　the　relaxed　sparsity　of　speech　sources,　we　propose　a　dynamic　threshold-based　separation　approach　of　sparse　components　where　the　threshold　is　determined　by　the　inter-channel　correlation　among　the　recording　signals.　After　conducting　a　statistical　analysis　of　the　number　of　active　sources　at　each　TF　instant,　a　form　of　relaxed　sparsity　called　the　half-K　assumption　is　proposed　so　that　the　active　source　number　in　a　certain　TF　bin　does　not　exceed　half　the　total　number　of　simultaneously　occurring　sources.　By　applying　the　half-K　assumption,　the　non-sparse　components　are　recovered　by　regarding　the　extracted　sparse　components　as　a　guide,　combined　with　vector　decomposition　and　matrix　factorization.　Eventually,　the　final　TF　coefficients　of　each　source　are　recovered　by　the　synthesis　of　sparse　and　non-sparse　components.　The　proposed　method　has　been　evaluated　using　up　to　six　simultaneous　speech　sources　under　both　anechoic　and　reverberant　conditions.　Both　objective　and　subjective　evaluations　validated　that　the　perceptual　quality　of　the　separated　speech　by　the　proposed　approach　outperforms　existing　blind　source　separation　(BSS)　approaches.　Besides,　it　is　robust　to　different　speeches　whilst　confirming　all　the　separated　speeches　with　similar　perceptual　quality.