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Mendelian randomization (MR) is a powerful approach to examine the causal relationships between health risk factors and outcomes from observational studies. Due to the proliferation of genome-wide association studies (GWASs) and abundant fully accessible GWASs summary statistics, a variety of two-sample MR methods for summary data have been developed to either detect or account for horizontal pleiotropy, primarily based on the assumption that the effects of variants on exposure (γ) and horizontal pleiotropy (α) are independent. This assumption is too strict and can be easily violated because of the correlated horizontal pleiotropy (CHP). To account for this CHP, we propose a Bayesian approach, MR-Corr2, that uses the orthogonal projection to reparameterize the bivariate normal distribution for γ and α, and a spike-slab prior to mitigate the impact of CHP. We develop an efficient algorithm with paralleled Gibbs sampling. To demonstrate the advantages of MR-Corr2 over existing methods, we conducted comprehensive simulation studies to compare for both type-I error control and point estimates in various scenarios. By applying MR-Corr2 to study the relationships between pairs in two sets of complex traits, we did not identify the contradictory causal relationship between HDL-c and CAD. Moreover, the results provide a new perspective of the causal network among complex traits. The developed R package and code to reproduce all the results are available at https://github.com/QingCheng0218/MR.Corr2.