An improved method for separation of fetal electrocardiogram (fECG) from abdominal electrocardiogram (abdECG) is proposed in this paper. Proposed method combines two widely used techniques i.e. compressive sensing (CS) and independent component analysis (ICA). Separation of fECG is carried out by applying ICA directly on the compressed signal. The efficient improved ℓp-regularized least-sqaures (ℓp-RLS) algorithm is used for signal reconstruction, which provides better reconstruction quality and less processing time in comparison with other existing methods. The proposed algorithm is evaluated and tested on Physionet datasets which contain 75 records in set-A, 100 records in set-B and 6 records in Silesia dataset. The obtained outcomes reveal that proposed algorithm shows promising results (Sensitivity S=92%, Positive predictivity P+ = 93%, F1 measure = 92.5% with average percentage root-mean-square difference PRD =6.89% and Execution time= 2.91 sec.). The results also indicate that there is a substantial improvement in quality of reconstructed signal which is achieved by maintaining lowest PRD.