We consider the problem of recovering block sparse signals with unknown block partition and propose a better alternative to the extended block sparse Bayesian learning (EBSBL). The underlying relationship between the proposed method EBSBL and pattern-coupled sparse Bayesian learning (PC-SBL) is explicitly revealed. The proposed method adopts a cluster-structured prior for sparse coefficients, which encourages dependencies among neighboring coefficients by properly manipulating the hyperparameters of the neighborhood. Due to entanglement of the hyperparameters, a joint sparsity assumption is made to yield a suboptimal analytic solution. The alternative algorithm avoids high dictionary coherence in EBSBL, reduces the unknowns of EBSBL, and explains the effectiveness of EBSBL. The proposed algorithm also avoids the vulnerability of parameter choice in PC-SBL. Results of comprehensive simulations demonstrate that the proposed algorithm achieves performance that is close to the best performance of PC-SBL. In addition, it outperforms EBSBL and other recently reported algorithms particularly under noisy and low sampling scenarios.