Core region detection of handwritten cursive words is an important step towards their automatic recognition. Several preprocessing operations such as height normalization, slant estimation etc. are often based on this core region. This is particularly useful for word recognition of major Indian scripts, which have large character sets. The main parts of majority of these characters belong to the core region that is bounded above by a headline and bounded below by an imaginary base line. Only a few such characters or their parts appear either above or below the core region. A few approaches are available in the literature for detection of such a core region of offline handwritten word samples of Latin script. Also, a similar region is often determined for recognition of images of printed Indian scripts. However, none of these approaches have studied detection of core region of an unconstrained online handwritten word. In this article, we propose a novel method for detection of the core region of online handwritten word samples of Bangla, a major Indian script. For this we first perform smoothing on the samples and then segment a stroke into substrokes. We compute certain novel positional features from each such substroke. Using these features, a multilayer perceptron (MLP) is trained by backpropagation (BP) algorithm. On the basis of the output of the MLP,we determine the position of both the headline and the baseline. We have tested this approach on a recently developed large database of online unconstrained handwriting Bangla word samples. The proposed approach would also work on similar samples of Devanagari, another major Indian script. Experimental results are encouraging.