The Rivest Cipher 4 (RC4) has been one of the most popular stream ciphers for providing symmetric key encryption, and is now proposed as an efficient cipher within light-weight cryptography. As an algorithm it has been considered to be one of the fastest stream ciphers and one of the easiest to implement. Unfortunately, despite its simplicity of usage, a number of attacks on it have been found. Therefore, various improvements of this algorithm exist in cryptography, but none of them use proper randomness. This paper outlines modified version of RC4 and which has the desirable features of an efficient stream cipher algorithm, and which integrates the Symmetric Random Function Generator (SRFG) method. Though RC4 uses pseudorandom features with an initialisation vector and a seed value, the use of true randomness in RC4 is novel in this domain. Therefore, this paper proposes a modified RC4 as MRC4, and which then evaluates the statistical features of MRC4 based upon parameters such as non-linearity, resiliency, balancedness, propagation and immunity. Further, we have compared the security features and confusiondiffusion attributes with some recent variants of RC4 and have found that MRC4 is efficient in withstanding against attacks. The experimental results show that MRC4 supports a 60% better confusion property and 50% better diffusion as compared to the original RC4 method.