You have not described what you want to see, only that the code creates what you do not like. Having guessed that you want to see mtext , create a "main name" that is further from the outer edge of the graphics device (closer to the graphs), I suggest you use a negative line number to place it. As the man page says, “line” indicates “starting at 0 counts” (although I could not find a description of where we should expect the zero line to be.)
par(mfrow=c(1,2)) # 1X2 graphs par(oma=c(0,0,5,0)) # top has 5 lines of space par(mar=c(4,4,2,1)+.1) # margin lines par(pin=c(1.9,1.9)) # plot areas for graphs # plot 1 plot(rnorm(n=20),col="olivedrab",pch=19,ylim=c(-2.0,2.0),xlim=c(0,20),ylab="",xlab="") mtext("Observation No.",side=1,line=3) mtext("Random variate",side=2,line=3) mtext("Olivedrab Plot",side=3,line=2,cex=1.5) # plot 2 plot(rnorm(n=20),col="olivedrab2",pch=19,ylim=c(-2.0,2.0),xlim=c(0,20),ylab="",xlab="") mtext("Observation No.",side=1,line=3) mtext("Random variate",side=2,line=3) mtext("Olivedrab Plot",side=3,line=2,cex=1.5) mtext("Army Olive Drab Plots",side=3,line=-3,cex=2,outer=TRUE)