No it isn't. If it is diluted 1:4 in tube 1, then a portion is diluted 1:4 again in tube 2, the final dilution is 1/4 x 1/4 = 1/16. You multiply successive dilutions, don't add. (Well, if you added, it would be 1/4 + 1/4 = 1/2, which is obvious nonsense.) But what I mean is if you do the same dilution twice, you don't double the dilution, you square it.
(On a pedantic point, I would say that the dilution in the first tube is 1:3, not 1:4 - i.e. 1 part sample to 3 parts diluent. That makes 1 part sample to 4 parts total, so the sample concentration is reduced by a factor of 4, so we call it a fourfold dilution. But when I spoke of multiplying, it is this factor that must be multiplied, so the second dilution gives a 16-fold diluted solution (1:15). It is not 1:9 i.e. 10-fold!)