Generally I'd say there is, but it's probably stronger for some types. There is a correlation between Big 5 and MBTI, and there is a correlation between MBTI and Socionics type, however:

- some russian articles show that the degree of perceived convergence between socionics and MBTI type is very strong for certain types and very weak for others.
- iterative application of a correlation function might lead to near-zero results and / or completely different ones