We study the Complementary Maximal Strip Recovery problem (CMSR), where the given are two strings S1 and S2 of distinct letters, each of which appears either in the positive form or the negative form. The question is whether there are k letters whose deletion results in two matched strings. String S1 matches string S2 if there are partitions of S1 and S2 such that each component of the partitions contains at least two letters and, moreover, for each component S1i of the partition of S1, there is a unique component S2j in the partition of S2 which is either equal to S1i or can be obtained from S1i by firstly reversing the order of the letters and then negating the letters. The CMSR problem is known to be NP-hard and fixed-parameter tractable with respect to k. In particular, a linear kernel of size 74k+4 was developed based on 8 reduction rules. Very recently, by imposing 3 new reduction rules to the previous kernelization, the linear kernel has been improved to 58k. We aim to simplify the kernelization, yet obtain an improved kernel. In particular, we study 7 reduction rules which lead to a linear kernel of size 42k+24.