Attempts to identify causal interactions in multivariable biological time series (e.g., gene data, protein data, physiological data) can be undermined by the confounding influence of environmental (exogenous) inputs. Compounding this problem, we are commonly only able to record a subset of all related variables in a system. These recorded variables are likely to be influenced by unrecorded (latent) variables. To address this problem, we introduce a novel variant of a widely used statistical measure of causality--Granger causality--that is inspired by the definition of partial correlation. Our 'partial Granger causality' measure is extensively tested with toy models, both linear and nonlinear, and is applied to experimental data: in vivo multielectrode array (MEA) local field potentials (LFPs) recorded from the inferotemporal cortex of sheep. Our results demonstrate that partial Granger causality can reveal the underlying interactions among elements in a network in the presence of exogenous inputs and latent variables in many cases where the existing conditional Granger causality fails.