In this paper, a one-to-one correspondence between the set of unit split semi-quaternions and unit tangent bundle of semi-Euclidean plane is given. It is shown that the set of unit split semi-quaternions based on the group operation of multiplication is a Lie group. The Lie algebra of this group, consisting of the vector space matrix of the angular velocity vectors, is also considered. Planar rotations in Euclidean plane are expressed using split semi-quaternions. Some examples are given to illustrate the findings.