A search for squarks in R-parity violating supersymmetry has been performed in e^{\pm} p collisions at HERA using the H1 detector.The data taken at a centre of mass energy of 319\,\GeV correspond to an integrated luminosity of 63.5\,\mathrm{pb^{-1}} for e^+p collisions and 13.5\,\mathrm{pb^{-1}} for e^-p collisions. The resonant production of squarks via a Yukawa coupling \lambda' has been considered and various decay topologies of squarks have been investigated. No significant deviation from the Standard Model has been found. The results are interpreted in terms of exclusion limits within the Minimal Supersymmetric Standard Model (MSSM) and the minimal Supergravity Model. All flavours of squarks have been searched for. Squark masses below 275\,\GeV are excluded at 95\,\% confidence level in a large part of the parameter space for a Yukawa coupling of electromagnetic strength.