Using the measured Raman spectra of triolein and cholesteryl linolenate, the contradiction caused in determining the
sequential orders in the two-dimensional correlation spectroscopy was exemplified, in which time-profiles of four
marker bands A, B, C, and D were modeled so that A→B→C→D. Here ‘A→B’ is such notation that we read as ‘A is
occurred before B’ or ‘A earlier than B’. The two-dimensional correlation method gave the result B→C→D→A which
was contradictive to the initial setting. We confirmed that the increments of distance between the peak positions of the
Gaussian type time-profiles ƒ and g, through a threshold, gave the unexpected switch in the sequential order. On the
complex plane based on the synchronous and asynchronous axes, the vector g is identical to the synchronous axis in
direction; the vector ƒ is crossed through the asynchronous axis corresponding to the increments of distance between the
peak positions of ƒ and g. By the conventional rule of the correlation method, the vector ƒ just crossing the asynchronous
axis is not allowed to be in the second quadrant, but the vector ƒ is transformed to the fourth quadrant with 180 degrees
shifted. In the situation, the vector ƒ is located in the later position for the standard vector g, that is, ƒ is occurred ‘after’ g.
Based on the revealed mechanism for the contradiction, the time series correlation analysis may be extended in a more
versatile manner to allow bio-Raman correlation analysis on diverse dynamics of bio-molecules in living cells.