  Using analytical methods and Monte Carlo simulations, we analyze a new
statistic designed to detect isolated step-like discontinuities which are
coherent over large areas of Cosmic Microwave Background (CMB) pixel maps. Such
coherent temperature discontinuities are predicted by the Kaiser-Stebbins
effect to form due to long cosmic strings present in our present horizon. The
background of the coherent step-like seed is assumed to be a scale invariant
Gaussian random field which could have been produced by a superposition of
seeds on smaller scales and/or by inflationary quantum fluctuations. The
effects of uncorrelated Gaussian random noise are also studied. The statistical
variable considered is the Sample Mean Difference (SMD) between large
neighbouring sectors of CMB maps, separated by a straight line in two
dimensional maps and a point in one dimensional maps. We find that including
noise, the SMD statistics can detect at the $1 \sigma$ to $2 \sigma$ level the
presense of a long string with $G\mu (v_s \gamma_s)= 1/(8\pi) ((\delta
T)/T)_{rms} \simeq 0.5 \times 10^{-7}$ while more conventional statistics like
the skewness or the kurtosis require a value of $G\mu$ almost an order of
magnitude larger for detectability at a comparable level.
