be a normed linear space and let $ x, y \in \mathbb{X}. $ We say that $ x $ is strongly orthogonal to $ y $ in the sense of Birkhoff-James, written as $ x \perp_{SB} y, $ if $ \| x + \lambda y \| > \| x \| $ for all $ \lambda \neq 0. $

Following the idea involved in the proof of Theorem 2.4 of [@SPJ], we observe that $ x \in S_{\mathbb{X}} $ is a rotund point of $ B_{\mathbb{X}} $ if and only if for any $ y \in \mathbb{X} \setminus \{\theta\}, $ $ x \perp_{B} y $ implies that $ x \perp_{SB} y. $ Equipped with this characterization of rotund points, we proceed towards obtaining a complete characterization of Birkhoff-James orthogonality of rotund points in the space of bounded linear operators. In order to obtain the desired characterization for rotund points and for general bounded linear operators, we need to introduce a new definition which is essentially geometric in nature. First, let us give a brief motivation in this regard. The notion of approximate orthogonality ($ \epsilon $-orthogonality) was first considered by Chmieliński in [@C]:\
Let $\mathbb{H}$ be an inner product space and 