  A scheme to form a basis and a frame for a Hilbert space of quaternion valued
square integrable function from a basis and a frame, respectively, of a Hilbert
space of complex valued square integrable functions is introduced. Using the
discretization techniques for 2D-continuous wavelet transform of the $SIM(2)$
group, the quaternionic continuous wavelet transform, living in a complex
valued Hilbert space of square integrable functions, of the quaternion wavelet
group is discretized, and thereby, a discrete frame for quaternion valued
Hilbert space of square integrable functions is obtained.
