Globular clusters may host intermediate mass black holes (IMBHs) at their centres. Here, we propose a new method for their identification using millisecond pulsars (MSPs) as probes. We show that measuring the first (jerk) and second (jounce) derivatives of the accelerations of an ensemble of MSPs will let us infer the presence of an IMBH in a globular cluster better than measuring the sole accelerations. We test this concept by simulating a set of star clusters with and without a central IMBH to extract the distributions of the stellar jerks and jounces. We then apply this technique to the ensemble ofMSPs in the Galactic globular cluster 47 Tucanae. Current timing observations are insufficient to constrain the presence of an IMBH and can only be used to pose upper limits on its mass. But, with few more years of observations it will be possible to test for the presence of a central IMBH with mass smaller than similar to 1000 M-circle dot. We conclude that jerks and jounces help significantly in reducing the upper limit of the mass of IMBHs in Galactic globular clusters.