This study uses a Cook's distance type diagnostic statistic to identify unusual observations in a data set that unduly influence the estimation of a covariance matrix. Similar to many other deletion-type diagnostic statistics, this proposed measure is susceptible to masking or swamping effect in the presence of several unusual observations. In view of this, a forward search procedure based on the proposed measure to detect extreme observations that respectively influence the covariance matrix estimates computed from different subsets of the data set was developed. These identified observations are summarized in a stalactite plot, giving a comprehensive picture about the suspicious data points. The stalactite plot is further examined with an objective to identifying multiple influential observations in the data set. Several data sets taken from the literature are used to illustrate the practicability and applicability of the proposed procedure.