Despite decades of research, discovering instantaneous causal relationships from observational brain imaging data, such as spontaneous MEG energies or fMRI, remains a difficult problem. Popular methods, such as Granger Causality and Non-Gaussian Structural Equation Models (SEM), either are unable to handle instantaneous effects or do not work because the data are not non-Gaussian enough. Here, we propose a model with instantaneous causality for temporally dependent variables; these are both very common properties in neuroimaging data. Then, we propose a method to estimate the causal directions based on likelihood ratios, which are related to mutual information between the residual and data variables. We thus construct a simple decision criterion that allows for instantaneous causal discovery in time-dependent data. The proposed method is computationally and conceptually very simple, and we show with simulated data that it performs well even in the case of limited sample sizes, presumably due to the general optimality properties of likelihood. We further apply it to an MEG dataset from the Cam-CAN repository, for which the method gives consistent causal directionalities of energies both intra-subject and inter-subject, as measured by split-half tests. It also gives better performance than Granger causality and non-Gaussian SEM methods in a brain age prediction task. The results also demonstrate that our method might be useful in analyzing causal brain connectomes in functional brain-imaging data.